Related papers: Equilibrium states for Ma\~n\'e diffeomorphisms
We show that the robustly transitive diffeomorphisms constructed by Bonatti and Viana have unique equilibrium states for natural classes of potentials. In particular, we characterize the SRB measure as the unique equilibrium state for a…
This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium…
We consider a robust class of random non-uniformly expanding local homeomorphisms and H\"older continuous potentials with small variation. For each element of this class we develop the Thermodynamical Formalism and prove the existence and…
We show that a class of robustly transitive diffeomorphisms originally described by Ma\~{n}\'{e} are intrinsically ergodic. More precisely we obtain an open set of diffeomorphisms which fail to be uniformly hyperbolic, but nevertheless have…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…
This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems with Measures (IFSm). We study the spectral properties of the Transfer and Markov operators associated to a IFSm. We introduce variational formulations…
We prove robustness and uniqueness of equilibrium states for a class of partially hyperbolic diffeomorphisms with dominated splittings and H\"older continuous potentials with not very large oscillation.
We consider skew-products on $M\times \mathbb{T}^2$, where $M$ is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism. This class of dynamics includes the open sets of…
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…
Given a dynamical system with a uniformly hyperbolic (`chaotic') attractor, the physically relevant Sinai-Ruelle-Bowen (SRB) measure can be obtained as the limit of the dynamical evolution of the leaf volume along local unstable manifolds.…
We study thermodynamic formalism for topologically transitive partially hyperbolic systems in which the center-stable bundle satisfies a bounded expansion property, and show that every potential function satisfying the Bowen property has a…
In this paper we study the thermodynamic formalism of strongly transitive endomorphisms $f$, focusing on the set all expanding measures. In case $f$ is a non-flat $C^{1+}$ map defined on a Riemannian manifold, these are invariant…
For classical discrete systems under constant composition, a set of microscopic state dominantly contributing to thermodynamically equilibrium structure should depend on temperature and energy through Boltzmann factor, exp(-bE). Despite…
We construct a family of partially hyperbolic skew-product diffeomorphisms on $\mathbb{T}^3$ that are robustly transitive and admitting two physical measures with intermingled basins. In particularly, all these diffeomorphisms are not…
For a smooth map f of a compact interval I admitting an inducing scheme we establish a thermodynamical formalism, i.e., describe a class of real-valued potential functions $\phi$ on I which admit a unique equilibrium measure $\mu_\phi$. Our…
The basic elements of the mathematical theory of states of thermal equilibrium of infinite systems of quantum anharmonic oscillators (quantum crystals) are outlined. The main concept of this theory is to describe the states of finite…
Using an approach due to Bowen, Franco showed that continuous expansive flows with specification have unique equilibrium states for potentials with the Bowen property. We show that this conclusion remains true using weaker non-uniform…
Given the full shift over a countable state space on a countable amenable group, we develop its thermodynamic formalism. First, we introduce the concept of pressure and, using tiling techniques, prove its existence and further properties…
We prove a random Ruelle--Perron--Frobenius theorem and the existence of relative equilibrium states for a class of random open and closed interval maps, without imposing transitivity requirements, such as mixing and covering conditions,…