Hyperbolic measures and commuting maps in low dimension

Anatoly Katok

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We study invariant measures with non-vanishing Lyapunov characteristic exponents for commuting diffeomorphisms of compact manifolds. In particular we show that for k = 2, 3 no faithful ℤk real-analytic action on a k-dimensional manifold preserves a hyperbolic measure. In the smooth case similar statements hold for actions faithful on the support of the measure. Generalizations to higher dimension are proved under certain non-degeneracy conditions for the Lyapunov exponents.

Original languageEnglish (US)
Pages (from-to)397-411
Number of pages15
JournalDiscrete and Continuous Dynamical Systems
Volume2
Issue number3
DOIs
StatePublished - Jan 1 1996

Fingerprint

Faithful
Lyapunov Exponent
Characteristic Exponents
Nondegeneracy
Diffeomorphisms
Invariant Measure
Compact Manifold
Higher Dimensions
Generalization

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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Hyperbolic measures and commuting maps in low dimension. / Katok, Anatoly.

In: Discrete and Continuous Dynamical Systems, Vol. 2, No. 3, 01.01.1996, p. 397-411.

Research output: Contribution to journalArticle

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