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We consider a robust class of random non-uniformly expanding local homeomorphisms and Holder continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and uniqueness of equilibrium states among non-uniformly expanding measures. Moreover, we show that these equilibrium states and the random topological pressure vary continuously in this setting.
In the context of non-uniformly expanding maps, possibly with the presence of a critical set, we prove the existence of finitely many ergodic equilibrium states for hyperbolic potentials. Moreover, the equilibrium states are expanding measures. The t
We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic dynamics semi-conjugated to non-uniformly expanding maps. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with
For a Markov map of an interval or the circle with countably many branches and finitely many neutral periodic points, we establish conditional variational formulas for the mixed multifractal spectra of Birkhoff averages of countably many observables,
This work constructs symbolic dynamics for non-uniformly hyperbolic surface maps with a set of discontinuities $D$. We allow the derivative of points nearby $D$ to be unbounded, of the order of a negative power of the distance to $D$. Under natural g
We consider the transfer operators of non-uniformly expanding maps for potentials of various regularity, and show that a specific property of potentials (flatness) implies a Ruelle-Perron-Frobenius Theorem and a decay of the transfer operator of the