Higher-dimensional nonlinear thermodynamic formalism

TL;DR

This paper extends the nonlinear thermodynamic formalism to higher dimensions by replacing a potential with a family of potentials, establishing a variational principle and analyzing equilibrium measures.

Contribution

It introduces a higher-dimensional framework for nonlinear thermodynamic formalism, including new variational principles and equilibrium measure analysis.

Findings

Established a variational principle for the higher-dimensional formalism

Discussed existence and characterization of equilibrium measures

Analyzed the number of equilibrium measures in the new setting

Abstract

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.