Construction d'un difféomorphisme minimal d'entropie topologique non nulle

Abstract

Abstract We construct a real analytic diffeomorphism F α on a compact connected 4-dimensional manifold M , such that F α preserves a probability measure μ defined by a smooth volume form, F α is a minimal diffeomorphism of M and furthermore the metrical entropy of F α with respect to the measure μ is strictly positive. By a theorem of Goodwyn the topological entropy is also strictly positive. We write down the explicit formula of F α that depends on a parameter α ∈ T 1 . This parameter is chosen by Baire category.