On Stochastic Sea of the Standard Map

By A. Gorodetski. 2010

48 citations recorded by the source corpus.

AbstractConsider 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 Ω of full Hausdorff dimension. The set Ω is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that a stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ad02ac08f851db3586712b70d0d5a8dd80e09e4e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Lai-Sang Young

In Mathematical Physics

1. A. Blumenthal
2. Jinxin Xue
3. Lai-Sang Young
4. Tomasz Downarowicz
5. Andrew J. Majda
6. Rafail V. Abramov

In Statistical and Nonlinear Physics

1. A. Blumenthal
2. Jinxin Xue
3. Lai-Sang Young
4. Tomasz Downarowicz
5. Andrew J. Majda
6. Rafail V. Abramov

Citations in the corpus

• Lyapunov exponents for random perturbations of some area-preserving maps including the standard map (2017, background): “The best result known [Gor12] is that the LE of Φ L is positive on sets of Hausdorff dimension 2 (which are very far from having positive Lebesgue measure).”