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Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity
(2021-09-01)
We consider a wide family of non-uniformly expanding maps and hyperbolic Hölder continuous potentials. We prove that the unique equilibrium state associated to each element of this family is given by the eigenfunction of ...
Gibbs–Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction
(Elsevier, 2010-03)
We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as TKM=Ecu⊕Es, for which the center-unstable direction Ecu expands non-uniformly on some local unstable disk. We show that under ...
Markov structures for non-uniformly expanding maps on compact manifolds in arbitrary dimension
(2002)
We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov ...
Markov structures and decay of correlations for non-uniformly expanding dynamical systems
(Elsevier, 2005-12)
We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov ...
Equilibrium states for non-uniformly expanding maps: Decay of correlations and strong stability
(Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 2013)
We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps
where no Markov assumption is required. We show that the Ruelle–Perron–Frobenius operator acting ...
Random walks in static and markovian time-dependent random environment
(2014)
Firstly, we introduce ellipticity criteria for random walks in i.i.d. random environments,
under which we can extend the ballisticity conditions of Sznitman’s and the polynomial
effective criteria of Berger, Drewitz and ...
ON A GENERAL MANY-DIMENSIONAL EXCITED RANDOM WALK
(INST MATHEMATICAL STATISTICS, 2012)
In this paper we study a substantial generalization of the model of excited random walk introduced in [Electron. Commun. Probab. 8 (2003) 86-92] by Benjamini and Wilson. We consider a discrete-time stochastic process (X-n, ...