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 …

Our goal in this paper is to review the existing literature on homoclinic and heteroclinic
bifurcation theory for flows. More specifically, we shall focus on bifurcations from homoclinic …

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 …

It is very unusual for a mathematical or physical idea to disseminate into the society at large.
An interesting example is chaos theory, popularized by Lorenz's butterfly effect:“does the …

We prove that a singular-hyperbolic attractor of a $3 $-dimensional flow is chaotic, in two
different strong senses. First, the flow is expansive: if two points remain close at all times …

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 …

We introduce a class of vector fields on n-manifolds containing the hyperbolic systems, the
singular-hyperbolic systems on 3-manifolds, the multidimensional Lorenz attractors and the …

We prove that for any s> 0 the majority of C^s linear cocycles over any hyperbolic (uniformly
or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an …

Résumé Depuis le travail fondamental de Poincaré sur l'étude qualitative des équations
différentielles en 1881, l'idée de chercher la description du comportement à long terme des …

We give an affirmative answer to a problem of Liao and Mañé which asks whether, for a
nonsingular flow to loose the Ω-stability, it must go through a critical-element-bifurcation …