In broad terms, the goal of dynamics is to describe the long-term evolution of systems for
which an" infinitesimal" evolution rule, such as a differential equation or the iteration of a …

Adaptive specialization of mechanisms is so ubiquitous and so obvious in biology, at every
level of analysis, and for every kind of function, that no one thinks it necessary to call …

Récurrence et généricité Page 1 DOI: 10.1007/s00222-004-0368-1 Invent. math. 158, 33–104
(2004) Récurrence et généricité Christian Bonatti,Sylvain Crovisier Institut de Mathématiques …

We show that, for every compact n-dimensional manifold, n> 1, there is a residual subset of
Diff (M) of diffeomorphisms for which the homoclinic class of any periodic saddle of f verifies …

The book aims to provide a global perspective of this theory and make it easier for the
reader to digest the growing literature on this subject. This is not the first book on the subject …

Inspired by Lorenz'remarkable chaotic flow, we describe in this paper the structure of all C1
robust transitive sets with singularities for flows on closed 3-manifolds: they are partially …

Robust chaos is defined by the absence of periodic windows and coexisting attractors in
some neighborhoods in the parameter space of a dynamical system. This unique book …

A diffeomorphism-generic dynamics (in any dimension). Two of such consequences are the
following. For tame diffeomorphisms (generic diffeomorphisms with finitely many chain …

We prove that the chain-transitive sets of C 1-generic diffeomorphisms are approximated in
the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense …

We construct locally generic C1-diffeomorphisms of 3-manifolds with maximal transitive
Cantor sets without periodic points. The locally generic diffeomorphisms constructed also …