On stochastic sea of the standard map

Details On stochastic sea of the standard map On stochastic sea of the standard map

2010-07-08

arxiv.org/abs/1007.1474v1

Mathematics

Dynamical Systems

36 pages, 5 figures

Scientific paper

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set $\Omega$ of full Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.

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