Volume growth and entropy for c1 partially hyperbolic diffeomorphisms

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Abstract

We show that the metric entropy of a C1 diffeomorphism with a dominated splitting and with the dominating bundle uniformly expanding is bounded from above by the integrated volume growth of the dominating (expanding) bundle plus the maximal Lyapunov exponent from the dominated bundle multiplied by its dimension. We also discuss different types of volume growth that can be associated with an expanding foliation and relationships between them, specially when there exists a closed form non-degenerate on the foliation. Some consequences for partially hyperbolic diffeomorphisms are presented.

Original languageEnglish
Pages (from-to)3789-3801
Number of pages13
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume34
Issue number9
DOIs
StatePublished - 1 Jan 2014

Keywords

  • Entropy
  • Partially hyperbolic diffeomorphisms
  • Volume growth

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