On the example of the famous Lorenz system, the difficulties and opportunities of reliable
numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz …

This article attempts a unification of the two approaches that have dominated theoretical
climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear …

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 …

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 statistical limit laws for sequences of Birkhoff sums of the type∑ j= 0 n− 1 vn∘ T nj
where T n is a family of nonuniformly hyperbolic transformations. The key ingredient is a new …

We prove exponential decay of correlations for a class of C^ 1+ α C 1+ α uniformly
hyperbolic skew product flows, subject to a uniform nonintegrability condition. In particular …

We establish a sufficient condition for a continuous map, acting on a compact metric space,
to have a Baire residual set of points exhibiting historic behavior (also known as irregular …