ABSTRACT. -It has been known since the pioneering work of Jakobson and subsequent work by Benedicks and Carleson and others that a positive measure set of quadratic maps admit an absolutely continuous invariant measure.
Abstract. We study the decay of correlations for towers. Using Birkhoff's projective metrics, we obtain a rate of mixing of the form:where α(n) goes to zero in a way related to the asymptotic mass of upper floors, f is some Lipschitz norm and g 1 is some L 1 norm. The fact that the dependence on g is given by an L 1 norm is useful to study asymptotic laws of successive entrance times.
We estimate density and regression functions for weak dependant datas. Using an exponential inequality obtained in [DeP] and in [Mau2], we control the deviation between the estimator and the function itself. These results are applied to a large class of dynamical systems and lead to estimations of invariant densities and on the mapping itself.2000 Mathematics Subject Classification. 37A50, 60E15, 37D20.
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.