Showing papers by "Jorge Milhazes Freitas published in 2011"
TL;DR: The equivalence between hitting time statistics laws and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue was shown in this article.
Abstract: We prove the equivalence between the existence of a non-trivial hitting time statistics law and Extreme Value Laws in the case of dynamical systems with measures which are not absolutely continuous with respect to Lebesgue. This is a counterpart to the result of the authors in the absolutely continuous case. Moreover, we prove an equivalent result for returns to dynamically defined cylinders. This allows us to show that we have Extreme Value Laws for various dynamical systems with equilibrium states with good mixing properties. In order to achieve these goals we tailor our observables to the form of the measure at hand.
79 citations
TL;DR: In this paper, it was shown that in many cases stochastic-like behaviour itself implies that the system has certain non-trivial geometric properties, which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration.
72 citations
01 Jan 2011
TL;DR: In this paper, the authors consider multimodal interval maps with at least polynomial growth of the derivative along the critical orbit and show that for certain families of this type of maps the equilibrium states vary continuously in the weak* topology, when perturb the map within the respective family.
Abstract: We consider multimodal interval maps with at least polynomial growth of the derivative along the critical orbit. For these maps Bruin and Todd showed the existence and uniqueness of equilibrium states for the potential ϕ t : x → − tlog | Df(x) | , for t close to 1. We show that for certain families of this type of maps the equilibrium states vary continuously in the weak* topology, when we perturb the map within the respective family. Moreover, in the case t = 1, when the equilibrium states are absolutely continuous with respect to Lebesgue, we show that the densities also vary continuously in the L 1 − norm.
2 citations
01 Jan 2011
TL;DR: In this article, the authors studied the asymptotic distribution of the partial maximum of observable random variables evaluated along the orbits of particular dynamical systems, and showed the link between Extreme Value Theory and Hitting Time Statistics for discrete time non-uniformly hyperbolic systems.
Abstract: We study the asymptotic distribution of the partial maximum of observable random variables evaluated along the orbits of some particular dynamical systems. Moreover, we show the link between Extreme Value Theory and Hitting Time Statistics for discrete time non-uniformly hyperbolic dynamical systems. This relation allows to study Hitting Time Statistics with tools from Extreme Value Theory, and vice versa.