THE LOCAL STAR CONDITION FOR GENERIC TRANSITIVE DIFFEOMORPHISMS

-generic Diffeomorphisms

On the one hand, we prove that the spaces of C 1 symplectomor-phisms and of C 1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C 1 diffeomorphisms of the circle and a non-empty open set of C 1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralize...

Locally maximal homoclinic classes for generic diffeomorphisms

Let M be a closed smooth d(≥ 2) dimensional Riemannian 1 manifold and let f : M → M be a diffeomorphism. For C generic f , a 2 locally maximal homogeneous homoclinic class is hyperbolic. 3 M.S.C. 2010: 37C20; 37D20. 4

Transitive Partially Hyperbolic Diffeomorphisms on 3-Manifolds

Degree of recurrence of generic diffeomorphisms

We study the spatial discretizations of dynamical systems: can we recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of orbits with a fixed number of digits. We show that the dynamics of the discretizations of a C generic conservative diffeomorphism of the torus is very different from t...

Modulus of Analytic Classification for Unfoldings of Generic Parabolic Diffeomorphisms

In this paper we give a complete modulus of analytic classification under weak equivalence for generic analytic 1-parameter unfoldings of diffeomorphisms with a generic parabolic point. The modulus is composed of a canonical parameter associated to the family, together with an unfolding of the Ecalle–Voronin modulus. We then study the fixed points bifurcating from a parabolic point with nontriv...