A. Lopes

activity

19952025

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

68 citations · 316 across the 71 of their papers we have counts for

collaborators

Showing 2018Show all

5 papers · 1 filter

math.DS2018

The sectional curvature of the infinite dimensional manifold of Hölder equilibrium prababilities

Artur O. Lopes, Rafael O. Ruggiero

Here we consider the discrete time dynamics described by a transformation $T : M \to M$ , where $T$ is the shift and $M = {1, 2, ..., d}^{N}$ . It is known that the infinite-dimens…

math.DS2018

Explicit examples in Ergodic Optimization

Hermes H. Ferreira, Artur O. Lopes, Elismar R. Oliveira

Denote by $T$ the transformation $T (x) = 2 x$ (mod 1). Given a potential $A : S^{1} \to R$ we are interested in exhibiting in several examples the explicit expression for th…

math.DS2018

An iterative process for approximating subactions

Hermes H. Ferreira, Artur O. Lopes, Elismar R. Oliveira

We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point w…

math.DS2018

Quantum Spin probabilities at positive temperature are Hölder Gibbs probabilities

Jader E. Brasil, Artur O. Lopes, Jairo K. Mengue +1

We consider the KMS state associated to the Hamiltonian $H = σ^{x} \otimes σ^{x}$ over the quantum spin lattice $C^{2} \otimes C^{2} \otimes C^{2} \otimes ...$ . For…

math.DS2018

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

Leandro Cioletti, L. Y. Hataishi, Artur O. Lopes +1

In this paper we study spectral triples and non-commutative expectations associated to expanding and weakly expanding maps. In order to do so, we generalize the Perron-Frobenius-Ru…