Hyperbolic measures and commuting maps in low dimension

Anatole Katok

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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
Issue number3
StatePublished - 1996

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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