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

Abstract

AbstractWe construct a real analytic diffeomorphismFαon a compact connected 4-dimensional manifoldM, such thatFαpreserves a probability measure μ defined by a smooth volume form,Fαis a minimal diffeomorphism ofMand furthermore the metrical entropy ofFαwith 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 ofFαthat depends on a parameter α ∈ T1. This parameter is chosen by Baire category.