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 describe a method for proving subexponential lower bounds for correlations functions,
and apply it to study decay of correlations for maps with countable Markov partitions. One …

We prove an almost sure invariance principle that is valid for general classes of
nonuniformly expanding and nonuniformly hyperbolic dynamical systems. Discrete time …

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 …

We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary
dimension, possibly having discontinuities and/or critical sets, and show that under some …

In Young towers with sufficiently small tails, the Birkhoff sums of Hölder continuous functions
satisfy a central limit theorem with speed O (1/n), and a local limit theorem. This implies the …

A classic approach in dynamical systems is to use particular geometric structures to deduce
statistical properties, for example the existence of invariant measures with stochastic-like …

We study geometric and statistical properties of complex rational maps satisfying a non-
uniform hyperbolicity condition called “Topological Collet–Eckmann”. This condition is …

We say that a rational function F satisfies the summability condition with exponent α if for
every critical point c which belongs to the Julia set J there exists a positive integer nc so that …

We consider partially hyperbolic C1+ diffeomorphisms of compact Riemannian manifolds of
arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition Es⊕ …