Geometric Expansions, Lyapunov Exponents and Foliations

Details Geometric Expansions, Lyapunov Exponents and Foliations Geometric Expansions, Lyapunov Exponents and Foliations

2006-11-11

arxiv.org/abs/math/0611324v1

Mathematics

Dynamical Systems

Scientific paper

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.

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