On the predictability of discrete dynamical systems III

Given an integer n 2, a metrizable compact topological n-manifold X with boundary and a finite positive Borel measure μ on X, we prove that “most” homeomorphisms f :X→X are non-sensitive μ-almost everywhere on X. Moreover, we also prove that for “most” homeomorphisms f :X→X the non-wandering set Ωf has μ-measure zero. © 2007 Elsevier Inc. All rights reserved