Add to ORKGWe discuss the thermodynamic formalism, i.e., an adaptation of the formalism of equilib-rium statistical physics to dynamical systems. It was developed in the classical works of Sinai, Ruelle, and Bowen and it deals with a continuous map $f $ of a compact metric space $X $ and a continuous function $¥varphi $ on $X $. Its main constituent components are: 1) the topological pressure $P(¥varphi);2) $ the variational principle, $P(¥varphi)=¥sup_{¥mu}E(¥varphi, ¥mu) $ where $ E(¥varphi, ¥mu)=h_{¥mu}(f)+¥int_{X}¥varphi d¥mu $ is (up to a normalizing factor) the free energy and the supremum is taken over all /-invariant Borel probability measures on $X;3 $ ) the equilibrium measures $¥mu_{¥varphi} $ for $¥varphi $ for which the above supremum is ...
ABSTRACT The formalism of the classical thermodynamics, for example Gibbs equations, is routinely an...
We study two classes of dynamical systems with holes: expanding maps of the interval and Collet-Eckm...
Let $X$ be a compact space, $f\colon X \to X$ a continuous map, and $\Lambda \subset X$ be any $f$-i...
Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classi...
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the st...
Given a finite-to-one map acting on a compact metric space, one classically constructs for each pote...
We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical s...
We relate the concepts of entropy and pressure to that of KMS states for C∗-algebras. Several differ...
This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal map...
This article proves that the dynamical system (f,μφ) enjoys exponential decay of correlations of Höl...
Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X...
We present the state of the art on the modern mathematical methods of exploiting the entropy princip...
We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical syst...
We present the state of the art on the modern mathematical methods of exploiting the entropy princip...
Consider a multidimensional shift space with a countably infinite alphabet, which serves in mathemat...
ABSTRACT The formalism of the classical thermodynamics, for example Gibbs equations, is routinely an...
We study two classes of dynamical systems with holes: expanding maps of the interval and Collet-Eckm...
Let $X$ be a compact space, $f\colon X \to X$ a continuous map, and $\Lambda \subset X$ be any $f$-i...
Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classi...
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the st...
Given a finite-to-one map acting on a compact metric space, one classically constructs for each pote...
We study continuity, and lack thereof, of thermodynamical properties for one-dimensional dynamical s...
We relate the concepts of entropy and pressure to that of KMS states for C∗-algebras. Several differ...
This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal map...
This article proves that the dynamical system (f,μφ) enjoys exponential decay of correlations of Höl...
Discrete dynamical systems are given by the pair (X, f ) where X is a compact metric space and f : X...
We present the state of the art on the modern mathematical methods of exploiting the entropy princip...
We study the Fluctuation Theorem (FT) for entropy production in chaotic discrete-time dynamical syst...
We present the state of the art on the modern mathematical methods of exploiting the entropy princip...
Consider a multidimensional shift space with a countably infinite alphabet, which serves in mathemat...
ABSTRACT The formalism of the classical thermodynamics, for example Gibbs equations, is routinely an...
We study two classes of dynamical systems with holes: expanding maps of the interval and Collet-Eckm...
Let $X$ be a compact space, $f\colon X \to X$ a continuous map, and $\Lambda \subset X$ be any $f$-i...