Lyapunov exponents for random perturbations of some area-preserving maps including the standard map

Alex Blumenthal, Jinxin Xue, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

We consider a large class of 2D area-preserving dieomorphisms that are not uniformly hyperbolic but have strong hyperbolicity properties on large regions of their phase spaces. A prime example is the standard map. Lower bounds for Lyapunov exponents of such systems are very hard to estimate, due to the potential switching of "stable" and "unstable" directions. This paper shows that with the addition of (very) small random perturbations, one obtains with relative ease Lyapunov exponents reflecting the geometry of the deterministic maps.

Original languageEnglish (US)
Pages (from-to)285-310
Number of pages26
JournalAnnals of Mathematics
Volume185
Issue number1
DOIs
StatePublished - 2017

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Standard Map
Random Perturbation
Lyapunov Exponent
Hyperbolicity
Small Perturbations
Phase Space
Unstable
Lower bound
Estimate
Perturbation
Lyapunov exponent
Class
Lower bounds
Geometry

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Lyapunov exponents for random perturbations of some area-preserving maps including the standard map. / Blumenthal, Alex; Xue, Jinxin; Young, Lai-Sang.

In: Annals of Mathematics, Vol. 185, No. 1, 2017, p. 285-310.

Research output: Contribution to journalArticle

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