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The School of Natural and Computing Sciences

Professor Celso Grebogi

Professor Celso Grebogi
Professor Celso Grebogi
Professor Celso Grebogi

CEng, MS, PhD, Drhc-mult, FRSE, FTWAS, MAE, FABC, FAPS, FInstP

Sixth Century Chair in Nonlinear & Complex Systems

About
Email Address
grebogi@abdn.ac.uk
Telephone Number
+44 (0)1224 272791
Office Address

Institute for Complex Systems and Mathematical Biology

King's College, University of Aberdeen

Old Aberdeen AB24 3UE, UK

School/Department
School of Natural and Computing Sciences
ORCiD
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Personal Website

Biography

Professor Celso Grebogi is the Sixth Century Chair at King’s College, University of Aberdeen, UK. He is the Founding Director of the Institute for Complex Systems and Mathematical Biology, whose work in systems biology and complex systems became leading in UK. He is the Co-founder of the Aberdeen-Lanzhou-Tempe Research Centre, whose work is in the new interdisciplinary field: Relativistic Quantum Chaos. He has been an External Scientific Member (Mitglied) of the Max-Planck-Society since 1998. He got his PhD in Theoretical Physics from the University of Maryland in 1978, Postdoc in Physics and Applied Mathematics at UC Berkeley in 1978-1981. He was at the University of Sao Paulo as Professor of Physics, and, before that, with the University of Maryland as Professor of Mathematics. He is a leading expert in chaotic and complex nonlinear dynamics, including fractal geometry and complex networks. He has made a huge impact in the area of control of chaos. His seminal paper was selected by Physical Review Letters as a milestone in the past 50 years. He was awarded the Citation Laureate - Researcher of Nobel Class - in 2016, followed by a Motion to that effect supported by the Scottish Parliament. His scientific accomplishments include over 500 publications and over 500 invited talks. He received numerous distinctions, including multiple Doctor Honoris Causa and many Honorary Professorships, the Humboldt Senior Prize, Fulbright Fellowship, and Toshiba Chair as a World-renown Scholar, the Lagrange Award, the Max-Planck-Society Badge of Honour, and the James Yorke Award. He is Fellow in various scientific societies, including the Royal Society of Edinburgh, The World Academy of Sciences, the Academia Europaea, the Brazilian Academy of Sciences, The American Physical Society and the UK Institute of Physics. He has 32,000 citations and h-index = 84 in Scopus, and 47,000 citations and h-index = 96 in Google Scholar.

 

Memberships and Affiliations

Internal Memberships

 

  • BSc, Chemical Engineering, Federal University of Parana, 1970
  • Adjunct Professor, Pontifical Catholic University, 1971-1974
  • M.S., Physics, University of Maryland 1975
  • Ph.D., Physics, University of Maryland, 1978
  • Post-doctoral Research Fellow, University of California at Berkeley, 1978-1981
  • Research Scientist, University of Maryland, 1981-1990
  • Associate Professor of Mathematics, University of Maryland, 1990-1993
  • Full Professor of Mathematics, University of Maryland, 1993-2001
  • Consultant for the US Navy, 1983-1995
  • Visiting Scientist, University of California at Santa Barbara, 1984
  • Consultant, Lawrence Livermore National Laboratory, 1984-1985
  • Consultant, Science Applications International, 1986-1988
  • Visiting Scholar, Waseda University, 1996
  • Visiting Professor, University of Potsdam, 1996-1997
  • External Scientific Member (Mitglied), Max-Planck-Society, since 1998
  • Professeur Invité, Université du Le Havre Normandie, 2001
  • Professor Titular, University of Sao Paulo, 2001-2005
  • Sixth Century Chair in Nonlinear and Complex Systems, University of Aberdeen, since 2005
  • Director of the Nonlinear Dynamics and Complex Systems Group. The Northern Research Partnership of Scottish Universities, 2007-2010
  • Founding Director of the Institute for Complex Systems and Mathematical Biology, since 2009
  • Visiting Professor, Institute of Medical Engineering, Xi'an Jiaotong University, 2010-2013
  • Senior Fellow of the Freiburg Institute for Advanced Studies, 2011-2013
  • Co-founder of the Aberdeen-Lanzhou-Tempe Joint Research Centre for Computation and Complexity, 2012
  • Visiting Professor, Xi'an University of Technology, since 2017

 

External Memberships

 

  • Fellow of the American Physical Society, 1991
  • Fellow of the Brazilian Academy of Sciences, 2003
  • Fellow of The World Academy of Sciences (TWAS/UNESCO), 2004
  • Fellow of the Institute of Physics (UK), 2011
  • Fellow of the Royal Society of Edinburgh, 2012
  • Member of the Academia Europaea, 2019
  • External Scientific Member (Mitglied), Max-Planck-Society, since 1998
  • Honorary Member of the International Physics and Control Society, 2009
  • Member of over a two dozen Editorial Boards and Associate Editorships over the years
  • Membership in various scientific societies

 

 

Prizes and Awards

 

  • Fulbright Fellowship Award, 1974
  • Distinguished Scientist Lecturer, Carnegie Mellon University, 1989
  • Toshiba Chair as World-renowned Scholar, 1995
  • Awarded the North British Differential Equations Lecture Tour, 1996
  • Senior Humboldt Prize, 1996
  • Distinguished Faculty Research Fellow Award, University of Maryland, 1996
  • Doctor Honoris Causa, University of Potsdam, Germany, 1997
  • Humboldt Prize Revisited Award, 2003
  • Controlling Chaos, Physical Review Letters selected it as a milestone  in the past 50 years, 2008
  • Honorary Professorship, Xi'an University of Technology, China, 2012
  • Honorary Pofessorship, Lanzhou University, China, 2012
  • Doctor Honoris Causa, Le Havre Normandie University, France, 2014
  • Honorary Professorship, Xi'an Jiaotong University, China, 2015
  • Awarded the Citation Laureate - Researcher of Nobel Class, 2016
  • Motion S5M-01678 supported in the Scottish Parliament: "Aberdeen Academic Included in Citation Laureate", 27/09/2016
  • Honorary Professorship, Tianjin University, China, 2018
  • Honorary Expert, Weifang/Weicheng City, Shandong, China, 2018
  • Honorary Professorship, Huaqiao Unviversity, China, 2018
  • Honorary Expert, National Institute of Metrology, Yantai, China, 2019
  • Burgess of Guild, The Burgesses of Guild of the City and Royal Burgh of Aberdeen, Scotland, 2022
  • Badge of Honour from the President of the Max-Planck-Society, 22 June 2023
  • Lagrange Award for Lifetime Achievement in Nonlinear Physical Science, 10 July 2023
  • James Yorke Award for for breakthrough achievements in Nonlinear Dynamics and Chaos, 22 June 2024
  • Scopus: 32,000 citations in indexed journals, h-index = 84
  • Google Scholar: 47,000 citations, h-index = 96

 

Research

Research Overview

Dynamics of nonlinear and complex systems including chaotic dynamics, fractal geometry, systems biology, population dynamics, neurodynamics, fluid advection, relativistic quantum nonlinear dynamics, and nanosystems.

Publications

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  • Converting transient chaos into sustained chaos by feedback control

    Lai, Y., Grebogi, C.
    Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, vol. 49, no. 2, pp. 1094-1098
    Contributions to Journals: Articles

  • CONTROL AND USE OF CHAOS

    GREBOGI, C., LAI, Y. C., Lai, Y.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • CONTROLLING TRANSIENT CHAOS IN DYNAMICAL SYSTEMS

    LAI, Y. C., GREBOGI, C., TEL, T., Lai, Y.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Controlling Chaos in Dynamical Systems

    Grebogi, C., Lai, Y. C.
    Proceedings of the Fifth International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • ON THE TENDENCY TOWARD ERGODICITY WITH INCREASING NUMBER OF DEGREES OF FREEDOM IN HAMILTONIAN SYSTEMS

    HURD, L., GREBOGI, C., OTT, E.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • ESTIMATING CORRELATION DIMENSION FROM A CHAOTIC TIME-SERIES - WHEN DOES PLATEAU ONSET OCCUR

    DING, M. Z., GREBOGI, C., OTT, E., SAUER, T., YORKE, J. A.
    Physica. D, Nonlinear Phenomena, vol. 69, no. 3-4, pp. 404-424
    Contributions to Journals: Articles

  • CRISIS IN CHAOTIC SCATTERING

    LAI, Y. C., GREBOGI, C., BLUMEL, R., KAN, I., Lai, Y.
    Physical Review Letters, vol. 71, no. 14, pp. 2212-2215
    Contributions to Journals: Articles

  • Conditions for the abrupt bifurcation to chaotic scattering

    Tel, T., Grebogi, C., Ott, E.
    Chaos, vol. 3, no. 4, pp. 495-503
    Contributions to Journals: Articles

  • Geometric mechanism for antimonotonicity in scalar maps with two critical points

    Dawson, S. P., Grebogi, C., Koçak, H.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 48, no. 3, pp. 1676-1682
    Contributions to Journals: Articles

  • GEOMETRIC MECHANISM FOR ANTIMONOTONICITY IN SCALAR MAPS WITH 2 CRITICAL-POINTS

    DAWSON, S. P., GREBOGI, C., KOCAK, H.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 48, no. 3, pp. 1676-1682
    Contributions to Journals: Articles

  • HOW OFTEN ARE CHAOTIC SADDLES NONHYPERBOLIC

    LAI, Y. C., GREBOGI, C., YORKE, J. A., KAN, I., Lai, Y.
    Nonlinearity, vol. 6, no. 5, pp. 779-797
    Contributions to Journals: Articles

  • Vertices in parameter space: Double crises which destroy chaotic attractors

    Gallas, J. A. C., Grebogi, C., Yorke, J. A.
    Physical Review Letters, vol. 71, no. 9, pp. 1359-1362
    Contributions to Journals: Articles

  • STABILIZING CHAOTIC-SCATTERING TRAJECTORIES USING CONTROL

    LAI, Y. C., TEL, T., GREBOGI, C., Lai, Y.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 48, no. 2, pp. 709-717
    Contributions to Journals: Articles

  • Plateau onset for correlation dimension: When does it occur?

    Ding, M., Grebogi, C., Ott, E., Sauer, T., Yorke, J. A.
    Physical Review Letters, vol. 70, no. 25, pp. 3872-3875
    Contributions to Journals: Articles

  • Using small perturbations to control chaos

    Shinbrot, T., Grebogi, C., Yorke, J. A., Ott, E.
    Nature, vol. 363, no. 6428, pp. 411-417
    Contributions to Journals: Articles

  • Communicating with chaos

    Hayes, S., Grebogi, C., Ott, E.
    Physical Review Letters, vol. 70, no. 20, pp. 3031-3034
    Contributions to Journals: Articles

  • SYNCHRONIZATION OF CHAOTIC TRAJECTORIES USING CONTROL

    LAI, Y. C., GREBOGI, C., Lai, Y.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 47, no. 4, pp. 2357-2360
    Contributions to Journals: Articles

  • TEMPORAL CROSSOVER FROM CLASSICAL TO QUANTUM BEHAVIOR - A MARKOV-CHAIN APPROACH

    LAI, Y. C., OTT, E., GREBOGI, C., Lai, Y.
    Physics Letters A, vol. 173, no. 2, pp. 148-152
    Contributions to Journals: Articles

  • Controlling Hamiltonian Chaos

    Lai, Y., Ding, M., Grebogi, C.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 47, no. 1, pp. 86-92
    Contributions to Journals: Articles

  • HIGHER-DIMENSIONAL TARGETING

    KOSTELICH, E. J., GREBOGI, C., OTT, E., YORKE, J. A.
    Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 47, no. 1, pp. 305-310
    Contributions to Journals: Articles

  • CODING INFORMATION IN THE NATURAL COMPLEXITY OF CHAOS

    HAYES, S., GREBOGI, C.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • CONTROLLING CHAOS IN HAMILTONIAN-SYSTEMS

    LAI, Y. C., DING, M. Z., GREBOGI, C., Lai, Y.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Evolution of Attractor Boundaries in Two-Dimensional Noninvertible Maps

    Chin, W., Kan, I., Grebogi, C.
    Random and Computational Dynamics, vol. 1, pp. 349-370
    Contributions to Journals: Articles

  • SYNCHRONIZATION OF A CHAOTIC OPTICAL-SYSTEM USING CONTROL

    LAI, Y. C., GREBOGI, C., Lai, Y.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • CONTROLLING CHAOS IN HIGH DIMENSIONAL SYSTEMS

    AUERBACH, D., GREBOGI, C., OTT, E., YORKE, J. A.
    Physical Review Letters, vol. 69, no. 24, pp. 3479-3482
    Contributions to Journals: Articles

  • Algebraic decay and fluctuations of the decay exponent in Hamiltonian systems

    Lai, Y., Ding, M., Grebogi, C., Blümel, R.
    Physical Review A, vol. 46, no. 8, pp. 4661-4669
    Contributions to Journals: Articles

  • Using chaos to target stationary states of flows

    Shinbrot, T., Grebogi, C., Ott, E., Yorke, J. A.
    Physics Letters A, vol. 169, no. 5, pp. 349-354
    Contributions to Journals: Articles

  • CONTROLLING CHAOTIC DYNAMIC-SYSTEMS

    ROMEIRAS, F. J., GREBOGI, C., OTT, E., DAYAWANSA, W. P.
    Physica. D, Nonlinear Phenomena, vol. 58, no. 1-4, pp. 165-192
    Contributions to Journals: Articles

  • Abrupt Dimension Changes at Basin Boundary Metamorphoses

    Park, B. S., Grebogi, C., Lai, Y.
    International Journal of Bifurcation and Chaos, vol. 2, no. 3, 533-541
    Contributions to Journals: Articles

  • QUANTUM MANIFESTATIONS OF CHAOTIC SCATTERING

    LAI, Y. C., BLUMEL, R., OTT, E., GREBOGI, C., Lai, Y.
    Physical Review Letters, vol. 68, no. 24, pp. 3491-3494
    Contributions to Journals: Articles

  • Algebraic decay and phase-space metamorphoses in microwave ionization of hydrogen Rydberg atoms

    Lai, Y., Grebogi, C., Blümel, R., Ding, M.
    Physical Review A, vol. 45, no. 11, pp. 8284-8287
    Contributions to Journals: Articles

  • Chaos in a Double Pendulum

    Shinbrot, T., Grebogi, C., Wisdom, J., Yorke, J. A.
    American Journal of Physics, vol. 60, no. 6, pp. 491-499
    Contributions to Journals: Articles

  • Determination of Crisis Parameter Values by Direct Observation of Manifold Tangencies

    Sommerer, J. C., Grebogi, C.
    International Journal of Bifurcation and Chaos, vol. 2, no. 2, pp. 383-396
    Contributions to Journals: Articles

  • Using the sensitive dependence of chaos (the ‘‘butterfly effect’’) to direct trajectories in an experimental chaotic system

    Shinbrot, T., Ditto, W., Grebogi, C., Ott, E., Spano, M., Yorke, J. A.
    Physical Review Letters, vol. 68, no. 19, pp. 2863-2866
    Contributions to Journals: Articles

  • Using Chaos to Direct Orbits to Targets in Systems Describable by a One-Dimensional Map

    Shinbrot, T., Ott, E., Grebogi, C., Yorke, J. A.
    Physical Review A, vol. 45, no. 6, pp. 4165-4168
    Contributions to Journals: Articles

  • Antimonotonicity: inevitable reversals of period-doubling cascades

    Dawson, S. P., Grebogi, C., Yorke, J. A., Kan, I., Kocak, H.
    Physics Letters A, vol. 162, no. 3, pp. 249-254
    Contributions to Journals: Articles

  • FEEDBACK-CONTROL OF CHAOTIC SYSTEMS

    ROMEIRAS, F. J., GREBOGI, C., OTT, E., DAYAWANSA, W. P.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • SUDDEN CHANGE IN THE SIZE OF CHAOTIC ATTRACTORS - HOW DOES IT OCCUR

    LAI, Y. C., GREBOGI, C., YORKE, J. A., Lai, Y.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Chaotic Scattering in Time-Dependent Hamiltonian Systems

    Lai, Y., Grebogi, C.
    International Journal of Bifurcation and Chaos, vol. 1, no. 3, pp. 667-679
    Contributions to Journals: Articles

  • Experimental confirmation of the scaling theory for noise-induced crises

    Sommerer, J. C., Ditto, W. L., Grebogi, C., Ott, E., Spano, M. L.
    Physical Review Letters, vol. 66, no. 15, pp. 1947-1950
    Contributions to Journals: Articles

  • EXPERIMENTAL CONFIRMATION OF THE THEORY FOR CRITICAL EXPONENTS OF CRISES

    SOMMERER, J. C., DITTO, W. L., GREBOGI, C., OTT, E., SPANO, M. L.
    Physics Letters A, vol. 153, no. 2-3, pp. 105-109
    Contributions to Journals: Articles

  • MASSIVE BIFURCATION OF CHAOTIC SCATTERING

    DING, M. Z., GREBOGI, C., OTT, E., YORKE, J. A.
    Physics Letters A, vol. 153, no. 1, pp. 21-26
    Contributions to Journals: Articles

  • SCALING LAW FOR CHARACTERISTIC TIMES OF NOISE-INDUCED CRISES

    SOMMERER, J. C., OTT, E., GREBOGI, C.
    Physical Review A, vol. 43, no. 4, pp. 1754-1769
    Contributions to Journals: Articles

  • Controlling Chaotic Dynamical Systems

    Romeiras, F. J., Ott, E., Grebogi, C., Dayawansa, W. P.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Controlling chaotic dynamical systems

    Romeiras, F. J., Ott, E., Grebogi, C., Dayawansa, W. P.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Cubic maps as models of two-dimensional antimonotonicity

    Dawson, S. P., Grebogi, C.
    Chaos, Solitons & Fractals, vol. 1, no. 2, pp. 137-144
    Contributions to Journals: Articles

  • Pointwise Dimension and Unstable Periodic Orbits

    Grebogi, C., Ott, E., Yorke, J. A.
    Essays on Classical and Quantum Dynamics: A Festschrift in Honor of Albert W.Saenz. Ellison, J., Uberall, H. (eds.). Gordon & Beach, pp. 57-62, 6 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Strange Saddles in Scattering Hamiltonian Systems

    Hsu, G. H., Bleher, S., Grebogi, C., Ott, E.
    em Essays on Classical and Quantum Dynamics. Gordon and Breach Science Publishers, pp. 63-69
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Using chaos to direct trajectories to targets

    Shinbrot, T., Ott, E., Grebogi, C., Yorke, J. A.
    Physical Review Letters, vol. 65, no. 26, pp. 3215-3218
    Contributions to Journals: Articles

  • Transition to chaotic scattering

    Ding, M., Grebogi, C., Ott, E., Yorke, J. A.
    Physical Review A, vol. 42, no. 12, pp. 7025-7040
    Contributions to Journals: Articles

  • Bifurcation to chaotic scattering

    Bleher, S., Grebogi, C., OTT, E.
    Physica. D, Nonlinear Phenomena, vol. 46, no. 1, pp. 87-121
    Contributions to Journals: Articles

  • Shadowing of physical trajectories in chaotic dynamics: Containment and refinement

    Grebogi, C., Hammel, S. M., Yorke, J. A., Sauer, T.
    Physical Review Letters, vol. 65, no. 13, pp. 1527-1530
    Contributions to Journals: Articles

  • Controlling chaos

    OTT, E., GREBOGI, C., YORKE, J. A.
    Physical Review Letters, vol. 64, no. 11, pp. 1196-1199
    Contributions to Journals: Articles

  • Multifractal properties of snapshot attractors of random maps

    Romeiras, F. J., Grebogi, C., Ott, E.
    Physical Review A, vol. 41, no. 2, pp. 784-799
    Contributions to Journals: Articles

  • Analyzing Chaos: A Visual Essay in Nonlinear Dynamics

    Grebogi, C., Ott, E., Varosi, F., Yorke, J. A.
    Energy Sciences Supercomputing. U.S. DOE National Energy Research Supercomputer Center
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • Controlling Chaotic Dynamical Systems

    Ott, E., Grebogi, C., Yorke, J. A.
    CHAOS: Soviet-American Perspective on Nonlinear Science. American Institute of Physics, pp. 153-172, 20 pages
    Chapters in Books, Reports and Conference Proceedings: Chapters

  • FRACTAL STRUCTURE IN PHYSICAL SPACE IN THE DISPERSAL OF PARTICLES IN FLUIDS

    YU, L., GREBOGI, C., OTT, E.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • CHAOTIC ATTRACTORS ON A 3-TORUS, AND TORUS BREAK-UP

    BATTELINO, P. M., GREBOGI, C., OTT, E., YORKE, J. A.
    Physica. D, Nonlinear Phenomena, vol. 39, no. 2-3, pp. 299-314
    Contributions to Journals: Articles

  • QUASIPERIODIC FORCING AND THE OBSERVABILITY OF STRANGE NONCHAOTIC ATTRACTORS

    ROMEIRAS, F. J., BONDESON, A., OTT, E., ANTONSEN, T. M., GREBOGI, C.
    Physica Scripta, vol. 40, no. 3, pp. 442-444
    Contributions to Journals: Articles

  • EXPERIMENTAL-OBSERVATION OF CRISIS-INDUCED INTERMITTENCY AND ITS CRITICAL EXPONENT

    DITTO, W. L., RAUSEO, S., CAWLEY, R., GREBOGI, C., HSU, G. H., KOSTELICH, E., OTT, E., SAVAGE, H. T., SEGNAN, R., SPANO, M. L., YORKE, J. A.
    Physical Review Letters, vol. 63, no. 9, pp. 923-926
    Contributions to Journals: Articles

  • ROUTES TO CHAOTIC SCATTERING

    BLEHER, S., OTT, E., GREBOGI, C.
    Physical Review Letters, vol. 63, no. 9, pp. 919-922
    Contributions to Journals: Articles

  • SCALING OF FRACTAL BASIN BOUNDARIES NEAR INTERMITTENCY TRANSITIONS TO CHAOS

    PARK, B. S., GREBOGI, C., OTT, E., YORKE, J. A.
    Physical Review A, vol. 40, no. 3, pp. 1576-1581
    Contributions to Journals: Articles

  • DIMENSIONS OF STRANGE NONCHAOTIC ATTRACTORS

    DING, M. Z., GREBOGI, C., OTT, E.
    Physics Letters A, vol. 137, no. 4-5, pp. 167-172
    Contributions to Journals: Articles

  • SPATIOTEMPORAL DYNAMICS IN A DISPERSIVELY COUPLED CHAIN OF NONLINEAR OSCILLATORS

    UMBERGER, D. K., GREBOGI, C., OTT, E., AFEYAN, B.
    Physical Review A, vol. 39, no. 9, pp. 4835-4842
    Contributions to Journals: Articles

  • THEORY OF 1ST ORDER PHASE-TRANSITIONS FOR CHAOTIC ATTRACTORS OF NONLINEAR DYNAMICAL-SYSTEMS

    OTT, E., GREBOGI, C., YORKE, J. A.
    Physics Letters A, vol. 135, no. 6-7, pp. 343-348
    Contributions to Journals: Articles

  • Evolution of attractors in quasiperiodically forced systems: From quasiperiodic to strange nonchaotic to chaotic

    Ding, M., Grebogi, C., Ott, E.
    Physical Review A, vol. 39, no. 5, pp. 2593-2598
    Contributions to Journals: Articles

  • EFFECT OF ELECTROMAGNETIC-FIELDS ON CHARGED-PARTICLE BEAM LIMITING CURRENT

    GREBOGI, C., UHM, H. S.
    Physics Letters A, vol. 135, no. 4-5, pp. 280-283
    Contributions to Journals: Articles

  • Chaos, Strange Attractors, and Fractal Basin Boundaries

    Grebogi, C.
    Transactions of the American Nuclear Society, vol. 60, pp. 346
    Contributions to Journals: Articles

  • Ponderomotive effects on charged particle beam limiting current

    Grebogi, C., Uhm, H. S.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • Calculation of limiting current in connection with application to gyrotron

    Uhm, H. S., Grebogi, C.
    Proceedings of SPIE, vol. 1039, pp. 233-234
    Contributions to Journals: Articles

  • Roundoff-induced periodicity and the correlation dimension of chaotic attractors

    Grebogi, C., Ott, E., Yorke, J. A.
    Physical Review A, vol. 38, no. 7, pp. 3688-3692
    Contributions to Journals: Articles

  • Numerical orbits of chaotic processes represent true orbits

    Hammel, S. M., Yorke, J. A., Grebogi, C.
    Bulletin of the American Mathematical Society, vol. 19, no. 2, pp. 465-469
    Contributions to Journals: Articles

  • MULTIPLE COEXISTING ATTRACTORS, BASIN BOUNDARIES AND BASIC SETS

    BATTELINO, P. M., GREBOGI, C., OTT, E., YORKE, J. A., YORKE, E. D.
    Physica. D, Nonlinear Phenomena, vol. 32, no. 2, pp. 296-305
    Contributions to Journals: Articles

  • Fractal boundaries for exit in Hamiltonian dynamics

    Bleher, S., Grebogi, C., Ott, E., Brown, R.
    Physical Review A, vol. 38, no. 2, pp. 930-938
    Contributions to Journals: Articles

  • CRITICAL EXPONENTS FOR POWER-SPECTRA SCALING AT MERGINGS OF CHAOTIC BANDS

    ROMEIRAS, F., GREBOGI, C., OTT, E.
    Physical Review A, vol. 38, no. 1, pp. 463-468
    Contributions to Journals: Articles

  • ENHANCEMENT OF LIMITING CURRENT OF CHARGED-PARTICLE BEAMS BY PONDEROMOTIVE ENERGY

    GREBOGI, C., UHM, H. S.
    Physics of Fluids, vol. 31, no. 5, pp. 1277-1279
    Contributions to Journals: Articles

  • Unstable periodic orbits and the dimensions of multifractal chaotic attractors

    Grebogi, C., Ott, E., Yorke, J. A.
    Physical Review A, vol. 37, no. 5, pp. 1711-1724
    Contributions to Journals: Articles

  • Strange saddles and the dimensions of their invariant-manifolds

    Hsu, G. H., Ott, E., Grebogi, C.
    Physics Letters A, vol. 127, no. 4, pp. 199-204
    Contributions to Journals: Articles

  • BASIC SETS - SETS THAT DETERMINE THE DIMENSION OF BASIN BOUNDARIES

    GREBOGI, C., NUSSE, H. E., OTT, E., YORKE, J. A.
    Lecture notes in mathematics, vol. 1342, pp. 220-250
    Contributions to Journals: Articles

  • CRITICAL EXPONENTS FOR CRISIS-INDUCED INTERMITTENCY

    GREBOGI, C., OTT, E., ROMEIRAS, F., YORKE, J. A.
    Physical Review A, vol. 36, no. 11, pp. 5365-5380
    Contributions to Journals: Articles

  • Basin boundary metamorphoses: Changes in accessible boundary orbits

    Grebogi, C., Ott, E., Yorke, J. A.
    Nuclear Physics B (Proceedings Supplements), vol. 2, no. C, pp. 281-300
    Contributions to Journals: Articles

  • THE GOODNESS OF ERGODIC ADIABATIC INVARIANTS

    BROWN, R., OTT, E., GREBOGI, C.
    Journal of Statistical Physics, vol. 49, no. 3-4, pp. 511-550
    Contributions to Journals: Articles

  • Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics

    Grebogi, C., Ott, E., Yorke, J. A.
    Science, vol. 238, no. 4827, pp. 632-638
    Contributions to Journals: Articles

  • Unstable periodic orbits and the dimension of chaotic attractors

    Grebogi, C., Ott, E., Yorke, J. A.
    Physical Review A, vol. 36, no. 7, pp. 3522-3524
    Contributions to Journals: Articles

  • ERGODIC ADIABATIC INVARIANTS OF CHAOTIC SYSTEMS

    BROWN, R., OTT, E., GREBOGI, C.
    Physical Review Letters, vol. 59, no. 11, pp. 1173-1176
    Contributions to Journals: Articles

  • SIMPLICIAL APPROXIMATION OF POINCARE MAPS OF DIFFERENTIAL-EQUATIONS

    VAROSI, F., GREBOGI, C., YORKE, J. A.
    Physics Letters A, vol. 124, no. 1-2, pp. 59-64
    Contributions to Journals: Articles

  • Do numerical orbits of chaotic dynamical processes represent true orbits?

    Hammel, S. M., Yorke, J. A., Grebogi, C.
    Journal of Complexity, vol. 3, no. 2, pp. 136-145
    Contributions to Journals: Articles

  • FRACTAL BASIN BOUNDARIES WITH UNIQUE DIMENSION

    GREBOGI, C., OTT, E., YORKE, J. A., NUSSE, H. E.
    Annals of the New York Academy of Sciences, vol. 497, pp. 117-126
    Contributions to Journals: Articles

  • Basin boundary metamorphoses: Changes in accessible boundary orbits

    Grebogi, C., Ott, E., Yorke, J. A.
    Physica. D, Nonlinear Phenomena, vol. 24, no. 1-3, pp. 243-262
    Contributions to Journals: Articles

  • Fractal basin boundaries

    Grebogi, C., Ott, E., Yorke, J. A.
    Lecture Notes in Physics, vol. 278, pp. 28-32
    Contributions to Journals: Articles

  • MULTI-DIMENSIONED INTERTWINED BASIN BOUNDARIES - BASIN STRUCTURE OF THE KICKED DOUBLE ROTOR

    GREBOGI, C., KOSTELICH, E., OTT, E., YORKE, J. A.
    Physica. D, Nonlinear Phenomena, vol. 25, no. 1-3, pp. 347-360
    Contributions to Journals: Articles

  • Ponderomotive Enhancement of Charged Particle Beam Limiting Current

    Grebogi, C., Uhm, H. S.
    Chapters in Books, Reports and Conference Proceedings: Conference Proceedings

  • QUASI-PERIODICALLY FORCED DYNAMIC-SYSTEMS WITH STRANGE NONCHAOTIC ATTRACTORS

    ROMEIRAS, F. J., BONDESON, A., OTT, E., ANTONSEN, T. M., GREBOGI, C.
    Physica. D, Nonlinear Phenomena, vol. 26, no. 1-3, pp. 277-294
    Contributions to Journals: Articles

  • MULTI-DIMENSIONED INTERTWINED BASIN BOUNDARIES AND THE KICKED DOUBLE ROTOR

    GREBOGI, C., KOSTELICH, E., OTT, E., YORKE, J. A.
    Physics Letters A, vol. 118, no. 9, pp. 448-452
    Contributions to Journals: Articles

  • PONDEROMOTIVE CONFINEMENT OF CHARGED-PARTICLE BEAMS IN A CYLINDRICAL WAVE-GUIDE

    GREBOGI, C., UHM, H. S.
    Physical Review A, vol. 34, no. 5, pp. 4083-4090
    Contributions to Journals: Articles

  • Critical Exponent of Chaotic Transients in Nonlinear Dynamical Systems

    Grebogi, C., Ott, E., Yorke, J. A.
    Physical Review Letters, vol. 57, no. 11, pp. 1284-1287
    Contributions to Journals: Articles

  • BROADENING OF SPECTRAL PEAKS AT THE MERGING OF CHAOTIC BANDS IN PERIOD-DOUBLING SYSTEMS

    BROWN, R., GREBOGI, C., OTT, E.
    Physical Review A, vol. 34, no. 3, pp. 2248-2254
    Contributions to Journals: Articles

  • Vlasov susceptibility of relativistic magnetized plasma and application to free‐electron lasers

    Grebogi, C., UHM, H. S.
    Physics of Fluids, vol. 29, no. 5, pp. 1748-1749
    Contributions to Journals: Articles

  • Metamorphoses of Basin Boundaries in Nonlinear Dynamical Systems

    Grebogi, C., Ott, E., Yorke, J. A.
    Physical Review Letters, vol. 56, no. 10, pp. 1011-1014
    Contributions to Journals: Articles

  • THE 2-PLASMON INSTABILITY FOR LOW-TEMPERATURE AND INHOMOGENEOUS-PLASMA

    GREBOGI, C., MANHEIMER, W. M.
    Plasma physics and controlled fusion, vol. 28, no. 2, pp. 439-451
    Contributions to Journals: Articles
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