Some remarks on the geometry of the Standard Map

Abstract

We define and compute hyperbolic coordinates and associated foliations which provide a new way to describe the geometry of the standard map. We also identify a uniformly hyperbolic region and a complementary 'critical' region containing a smooth curve of tangencies between certain canonical 'stable' foliations.

25 pages, 11 figures

Cited by in corpus (4)

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• Records and occupation time statistics for area-preserving maps
• Rigorous computation of expansion in one-dimensional dynamics
• Oseledets' Splitting of Standard-like Maps