Some apects of thermodinamic formalism of piecewise of smooth vector fields

TL;DR

This paper explores thermodynamic formalism for piecewise smooth vector fields, analyzing topological pressure, entropy, and their relation to Hausdorff dimensions using conjugation and Perron-Frobenius operators.

Contribution

It introduces new insights into the thermodynamic formalism of piecewise smooth vector fields, linking entropy, pressure, and fractal dimensions through novel analytical methods.

Findings

Established relationships between entropy and Hausdorff dimensions.

Applied topological conjugation with shift maps to analyze vector fields.

Utilized Perron-Frobenius operator to study thermodynamic properties.

Abstract

In this paper we study some aspects of thermodynamic formalism, more specifically topological pressure and, as a consequence, topological entropy for piecewise smooth vector fields, using topological conjugation with shift maps and the Perron- Frobenius Operator. Some relationships between entropy and Hausdorff dimensions are also investigated.