In this work we study the Ruelle Operator associated to a continuous potential defined on a
countable product of a compact metric space. We prove a generalization of Bowen's criterion …

In this paper, we describe several different meanings for the concept of Gibbs measure on
the lattice $\mathbb {N} $ in the context of finite alphabets (or state space). We compare and …

Ruelle's transfer operator plays an important role in understanding thermodynamic and
probabilistic properties of dynamical systems. In this work, we develop a method of finding …

It is well known that in Information Theory and Machine Learning the Kullback-Leibler
divergence, which extends the concept of Shannon entropy, plays a fundamental role. Given …

In this paper, we show a new relation between phase transition in Statistical Mechanics and
the dimension of the space of harmonic functions (SHF) for a transfer operator. This is …

In this paper we study the double transpose of the $ L^ 1 (X,\mathscr {B}(X),\nu) $-
extensions of the Ruelle transfer operator $\mathscr {L} _ {f} $ associated to a general real …

Consider a compact metric space (M, d M) and X= MN. We prove a Ruelle's Perron
Frobenius Theorem for a class of compact subshifts with Markovian structure introduced in …

In this paper, we provide sufficient conditions for the validity of the FKG Inequality, on
Thermodynamic Formalism setting, for a class of eigenmeasures of the dual of the Ruelle …

With view to applications, we here give an explicit correspondence between the following
two:(i) the set of symmetric and positive measures ρ on one hand, and (ii) a certain family of …

Consider a topologically transitive unilateral countable Markov shift $\Sigma $, a locally
constant potential $\phi:\Sigma\to\mathbb {R} $ satisfying suitable conditions, and assume …