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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 ϕt : 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,...
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...
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