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 …

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 …

The Lorenz Attractor is Mixing Page 1 Digital Object Identifier (DOI) 10.1007/s00220-005-1411-9
Commun. Math. Phys. 260, 393–401 (2005) Communications in Mathematical Physics 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 …

Chaotic attractors appear in various physical and biological models; however, rigorous
proofs of their existence and bifurcations are rare. In this paper, we construct a simple …

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 …

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 prove an almost sure invariance principle (approximation by d-dimensional Brownian
motion) for vector-valued Hölder observables of large classes of nonuniformly hyperbolic …

Dynamics: A Probabilistic and Geometric Perspective Page 1 Doc. Math. J. DMV 1 Dynamics: A
Probabilistic and Geometric Perspective Marcelo Viana1 Abstract. An overview of recent …

A rigorous numerical algorithm, formally verified with Isabelle/HOL, is used to certify the
computations that Tucker used to prove chaos for the Lorenz attractor. The verification is …