Non-hyperbolic equilibria and non-traversal homoclinic points of strongly nonlinear dynamical system

Non-hyperbolic equilibria and non-traversal homoclinic points of strongly nonlinear dynamical system

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Non-hyperbolic equilibria and non-traversal homoclinic points of strongly nonlinear dynamical systems

The properties of periodic solutions of strongly nonlinear systems, like vibro-impact systems or ones with a dry friction may change very quickly as one changes the parameters of the system. The ratios of their Lyapunov exponents may be big and even the dimensions of their stable and unstable manifolds may be difficult to be calculated. However, the theory of non-hyperbolic equilibria (and, more generally, one of the partial hyperbolicity) can be applied for the considered case. We start with a general case of a diffeomorphism of a smooth manifold or the Euclidean space and get a criteria of existence of invariant sets, containing infinite numbers of periodic points. These sets are not structurally stable, but the fact of their existence persists i.e. they may not completely disappear. The applications to vibro-impact systems are considered.

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Speaker
Dr Sergey Kryzhevich, Saint-Petersburg State University, Russia
Hosted by
CADR
Venue
FN 110