Ergodic optimization is the study of problems relating to maximizing orbits and invariant
measures, and maximum ergodic averages. An orbit of a dynamical system is called a larger …

Entropy and variational principle for one-dimensional lattice systems with a general a priori
probability: positive and zero tem Page 1 Ergod. Th. & Dynam. Sys. (2015), 35, 1925–1961 …

This book focuses on the interpretation of ergodic optimal problems as questions of
variational dynamics, employing a comparable approach to that of the Aubry-Mather theory …

We study the zero-temperature limit of the Gibbs measures of a class of long-range
potentials on a full shift of two symbols. These potentials were introduced by Walters as a …

Consider a topologically transitive countable Markov shift and, let $ f $ be a summable
potential with bounded variation and finite Gurevic pressure. We prove that there exists an …

R-POSITIVITY AND THE EXISTENCE OF ZERO-TEMPERATURE LIMITS OF GIBBS
MEASURES ON NEAREST-NEIGHBOR MATRICES Page 1 J. Appl. Probab. 1–20 (2023) …

We construct a short-range potential on a bidimensional full shift and finite alphabet that
exhibits a zero-temperature chaotic behaviour as introduced by van Enter and Ruszel. A …

In this paper we study ergodic optimization problems for subadditive sequences of functions
on a topological dynamical system. We prove that for t→∞ any accumulation point of a …

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 …

We consider transfer operators for topological Markov shift (TMS) with countable states and
with holes which are $2 $-cylinders. As main results, if the closed system of the shift has …