Geometric expansion, Lyapunov exponents and foliations

  • Radu Saghin

    Centre de Recerca Matematica, Apartat 50, Bellaterra, 08193, Spain
  • Zhihong Xia

    Department of Mathematics, Northwestern University, Evanston, IL 60208, USA

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.

Cite this article

Radu Saghin, Zhihong Xia, Geometric expansion, Lyapunov exponents and foliations. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 2, pp. 689–704

DOI 10.1016/J.ANIHPC.2008.07.001