Related papers: Thermodynamic Formalism for Generalized Countable …

Let $(\Omega,\mu)$ be a $\sigma$-finite measure space, and let $X\subset L^1(\Omega)+L^\infty(\Omega)$ be a fully symmetric space of measurable functions on $(\Omega,\mu)$. If $\mu(\Omega)=\infty$, necessary and sufficient conditions are…

We show that a shift space on a finite alphabet with a non-uniform specification property can be modeled by a strongly positive recurrent countable-state Markov shift to which every equilibrium state lifts. In addition to uniqueness of the…

Let $\sigma:\boldsymbol{\Sigma}\to\boldsymbol{\Sigma}$ be the left shift acting on $ \boldsymbol{\Sigma} $, a one-sided Markov subshift on a countable alphabet. Our intention is to guarantee the existence of $\sigma$-invariant Borel…

Let $T\in C^{2+\varepsilon}(S^{1}\setminus\{x_{b}\}),\,\,\varepsilon>0,$ be an orientation preserving circle homeomorphism with rotation number $\rho_T=[k_{1},k_{2},..,k_{m},1,1,...],\,\,m\geq1$, and a single break point $x_{b}$. We…

Let $\Sigma_{A}(\mathbb{N})$ be a topologically mixing countable Markov shift with the BIP property over the alphabet $\mathbb{N}$ and $f: \Sigma_{A}(\mathbb{N}) \rightarrow \mathbb{R}$ a potential satisfying the Walters condition with…

We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…

We develop a quenched thermodynamic formalism for a wide class of random maps with non-uniform expansion, where no Markov structure, no uniformly bounded degree or the existence of some expanding dynamics is required. We prove that every…

We consider new concepts of entropy and pressure for stationary systems acting on density matrices which generalize the usual ones in Ergodic Theory. Part of our work is to justify why the definitions and results we describe here are…

We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of probability spaces. It also gives an isomorphism between…

Working with well chosen Riemannian metrics and employing Nevanlinna's theory, we make the thermodynamical formalism work for a wide class of hyperbolic meromorphic functions of finite order (including in particular exponential family,…

Countable state Markov shifts are a natural generalization of the well-known subshifts of finite type. They are the subject of current research both for their own sake and as models for smooth dynamical systems. In this paper, we…

We study ergodic properties of certain piecewise smooth two-dimensional systems by constructing countable Markov partitions. Using thermodynamic formalism we prove exponential decay of correleations.

This paper is devoted to study how do thermodynamic formalism quantities varies for time changes of suspension flows defined over countable Markov shifts. We prove that in general no quantity is preserved. We also make a topological…

Starting from the full--shift on a finite alphabet $A$, mingling some symbols of $A$, we obtain a new full shift on a smaller alphabet $B$. This amalgamation defines a factor map from $(A^{\mathbb N},T_A)$ to $(B^{\mathbb N},T_B)$, where…

We give sufficient conditions for a shift space $(\Sigma,\sigma)$ to be intrinsically ergodic, along with sufficient conditions for every subshift factor of $\Sigma$ to be intrinsically ergodic. As an application, we show that every…

A numeration system originally implies a digitization of real numbers, but in this paper it rather implies a compactification of real numbers as a result of the digitization. By definition, a numeration system with $G$, where $G$ is a…

We study the finite volume/temperature correlation functions of the (1+1)-dimensional ${\rm SU}(N)$ principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large $N$, and…

We investigate different notions of recognizability for a free monoid morphism $\sigma: \mathcal{A}^* \to \mathcal{B}^*$. Full recognizability occurs when each (aperiodic) point in $\mathcal{B}^\mathbb{Z}$ admits at most one tiling with…

We prove asymptotic results for a modification of the cross-entropy estimator originally introduced by Ziv and Merhav in the Markovian setting in 1993. Our results concern a more general class of decoupled measures on shift spaces over a…

We introduce the multiplicative Ising model and prove basic properties of its thermodynamic formalism such as existence of pressure and entropies. We generalize to one-dimensional "layer-unique" Gibbs measures for which the same results can…