A volume preserving flow with essential coexistence of zero and non-zero Lyapunov exponents

Jianyu Chen, Huyi Hu, Yakov Pesin

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We demonstrate essential coexistence of hyperbolic and non-hyperbolic behavior in the continuous-time case by constructing a smooth volume preserving flow on a five-dimensional compact smooth manifold that has non-zero Lyapunov exponents almost everywhere on an open and dense subset of positive but not full volume and is ergodic on this subset while having zero Lyapunov exponents on its complement. The latter is a union of three-dimensional invariant submanifolds, and on each of these submanifolds the flow is linear with Diophantine frequency vector.

Original languageEnglish (US)
Pages (from-to)1748-1785
Number of pages38
JournalErgodic Theory and Dynamical Systems
Volume33
Issue number6
DOIs
StatePublished - Dec 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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