Rafael R. Souza

activity

20082022

most citedContinuous time finite state mean field games

137 citations · 408 across the 17 of their papers we have counts for

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9 papers · 1 filter

math.DS2022

Thermodynamic formalism for general iterated function systems with measures

Jader E. Brasil, Elismar R. Oliveira, Rafael Rigão Souza

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…

math.DS2020★ 1 cited

Existence of Gibbs states and maximizing measures on a general one-dimensional lattice system with markovian structure

Rafael Rigão Souza, Victor Vargas

Consider a compact metric space $(M, d_{M})$ and $X = M^{N}$ . We prove a Ruelle's Perron Frobenius Theorem for a class of compact subshifts with Markovian structure introduc…

math.DS2015

An Ergodic Theorem on Ergodic Transport

Joana Mohr, Rafael Rigão Souza

Here we present an ergodic theorem which adapts a Theorem by J. Elton to the classical thermodynamical formalism and to ergodic transport. First, we discuss how Elton's theorem can…

math.DS2014

Ergodic and Thermodynamic Games

Rafael R. Souza

Let $T : X \to X$ and $S : Y \to Y$ be continuous maps defined on compact sets. Let $φ_{i} (μ, ν) = \int_{X \times Y} A_{i} (x, y) d μ (x) d ν (y) f or i = 1, 2,$ where $μ$ is $T$ -invariant…

math.DS2013★ 1 cited

Entropy, Pressure and Duality for Gibbs plans in Ergodic Transport

A. O. Lopes, J. K. Mengue, J. Mohr +1

Let $X$ be a finite set and $Ω = {1, ..., d}^{N}$ be the Bernoulli space. Denote by $σ$ the shift map acting on $Ω$ . For a fixed probability $μ$ on $X$ with supp( $μ$ ) $= X$ , d…

math.DS2012★ 68 cited

Entropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature

Artur O. Lopes, Jairo K. Mengue, Joana Mohr +1

We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^\ma…

math.DS2012★ 11 cited

The Analyticity of a Generalized Ruelle's Operator

Eduardo Antonio da Silva, Raderson Rodrigues da Silva, Rafael Rigao Souza

In this work we propose a generalization of the concept of Ruelle operator for one dimensional lattices used in thermodynamic formalism and ergodic optimization, which we call gene…

math.DS2011★ 40 cited

On the general one-dimensional XY Model: positive and zero temperature, selection and non-selection

A. T. Baraviera, L. M. Cioletti, A. O. Lopes +2

We consider $(M, d)$ a connected and compact manifold and we denote by $B_{i}$ the Bernoulli space $M^{Z}$ of sequences represented by $$x=(... x_{-3},x_{-2},x_{-1},x_0,x_1…

math.DS2008★ 13 cited

Negative Entropy, Zero temperature and stationary Markov Chains on the interval

Artur O. Lopes, Joana Mohr, Rafael R. Souza +1

We analyze some properties of maximizing stationary Markov probabilities on the Bernoulli space $[0, 1]^{N}$ , More precisely, we consider ergodic optimization for a continuou…