Link to this article: http://journals.cambridge.org/abstract_S0143385711000897 How to cite this article: J.-R. CHAZOTTES and P. COLLET (2013). Poisson approximation for the number of visits to balls in non-uniformly hyperbolic dynamical systems.Abstract. We study the number of visits to balls B r (x), up to time t/µ(B r (x)), for a class of non-uniformly hyperbolic dynamical systems, where µ is the Sinai-Ruelle-Bowen measure. Outside a set of 'bad' centers x, we prove that this number is approximately Poissonnian with a controlled error term. In particular, when r → 0, we get convergence to the Poisson law for a set of centers of µ-measure one. Our theorem applies for instance to the Hénon attractor and, more generally, to systems modelled by a Young tower whose return-time function has an exponential tail and with one-dimensional unstable manifolds. Along the way, we prove an abstract Poisson approximation result of independent interest.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.