A Volume Preserving Diffeomorphism with Essential Coexistence of Zero and Nonzero Lyapunov Exponents

Abstract

We show that there exists a C∞ volume preserving topologically transitive diffeomorphism of a compact smooth Riemannian manifold which is ergodic (indeed is Bernoulli) on an open and dense subset \({\mathcal{G}}\) of not full volume and has zero Lyapunov exponent on the complement of \({\mathcal{G}}\) .