The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

RADU SAGHIN , Zhihong Xia

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one-dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

Original languageEnglish
Pages (from-to)29-34
Number of pages6
JournalTopology and its Applications
Volume157
Issue number1
DOIs
StatePublished - 1 Jan 2010

Keywords

  • Entropy conjecture
  • Partially hyperbolic diffeomorphisms
  • Volume growth

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