Geometric expansion, Lyapunov exponents and foliations

Radu Saghin, Zhihong Xia

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological invariants and the geometric and Lyapunov growths of these foliations. As an application, we show examples of systems with persistent non-absolute continuous center and weak unstable foliations. This generalizes the remarkable results of Shub and Wilkinson to cases where the center manifolds are not compact.

Original languageEnglish
Pages (from-to)689-704
Number of pages16
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume26
Issue number2
DOIs
StatePublished - 2009
Externally publishedYes

Keywords

  • Fubini's nightmare
  • Homology of foliations
  • Partially hyperbolic

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