Isentropic fitting of Anosov automorphisms

Abstract

AbstractIn response to a question of Newhouse, we show that in many cases an Anosov automorphism can be uniformly approximated by a Smale diffeomorphism of the same topological entropy. We conjecture this can be done whenever the automorphism is sufficiently hyperbolic.A three-dimensional example is given that suggests this approximation is not always possible.