Note on homology of expanding foliations

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Abstract

This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.

Original languageEnglish
Pages (from-to)349-360
Number of pages12
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume2
Issue number2
DOIs
StatePublished - 1 Jun 2009

Keywords

  • Expanding dynamics
  • Invariant foliations
  • Ruelle-Sullivan currents

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