arXiv subjects

Carllos Eduardo Holanda

Publications and source records attributed to Carllos Eduardo Holanda.

3 recordsLinked to original sources

arXiv2025

Nonadditive families of potentials: physical equivalence and some regularity relations

We show that additive and asymptotically additive families of continuous functions with respect to suspension flows are physically equivalent. In particular, the equivalence result holds for hyperbolic flows and some classes of expansive flows in general. Moreover, we show how this equivalence result can be used to extend the nonadditive thermodynamic formalism and multifractal analysis. In the second part of this work, we obtain a Livšic-like result for nonadditive families of potentials and also address the Hölder and Bowen regularity problem for the physical equivalence relations with respect to hyperbolic symbolic flows.

math.DS↗

arXiv2023

A Livšic-type theorem and some regularity properties for nonadditive sequences of potentials

We study some notions of cohomology for asymptotically additive sequences and prove a Livšic-type result for almost additive sequences of potentials. As a consequence, we are able to characterize almost additive sequences based on their equilibrium measures and also show the existence of almost (and asymptotically) additive sequences of Hölder continuous functions satisfying the bounded variation condition (with a unique equilibrium measure) and which are not physically equivalent to any additive sequence generated by a Hölder continuous function. None of these examples were previously known, even in the case of full shifts of finite type. Moreover, we also use our main result to suggest a classification of almost additive sequences based on physical equivalence relations with respect to the classical additive setup.

math.DS↗

arXiv2021

Higher-dimensional nonlinear thermodynamic formalism

We introduce a higher-dimensional version of the nonlinear thermodynamic formalism introduced by Buzzi and Leplaideur, in which a potential is replaced by a family of potentials. In particular, we establish a corresponding variational principle and we discuss the existence, characterization, and number of equilibrium measures for this higher-dimensional version.

math.DS↗