Positive Entropy Through Pointwise Dynamics

We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which are approximated by maps with the shadowing property in a uniform way.Comment: 8 page

A λ-lemma for foliations

AbstractWe show that a C0 codimension one foliation with C1 leaves F of a closed manifold is minimal if there are a foliation G transverse to F, and a diffeomorphism f preserving both foliations, such that every leaf of F intersects every leaf of G and f expands G. We use this result to study of Anosov actions on closed manifolds