Non-hyperbolic ergodic measures with the full support and positive entropy

Abstract

AbstractThe aim of this note is to give an alternative proof for the following result originally proved by Bonatti, Díaz and Kwietniak. For every $$n\ge 3$$ n ≥ 3 there exists a compact manifold without boundary $${\mathbf {M}}$$ M of dimension n and a non-empty open set $$U\subset \text {Diff}({\mathbf {M}})$$ U ⊂ Diff ( M ) such that for every $$f\in U$$ f ∈ U there exists a non-hyperbolic measure $$\mu $$ μ invariant for f with positive entropy and full support. We also investigate the connection between the Feldman-Katok convergence of measures and the Kuratowski convergence of their supports.