On the dynamics of certain actions of free groups on closed real analytic manifolds

Abstract

Let M be a closed connected real analytic manifold; let $\Gamma$ be a free group on two generators. The set of analytic actions of $\Gamma$ on M endowed with Taken‘s topology contains a nonempty open subset whose corresponding actions share three properties: (a) they have every orbit dense, (b) they leave invariant no geometric structure on M, (c) any homeomorphism conjugating two of them is analytic.