On the topological pressure of the saturated set with non-uniform structure

TL;DR

This paper establishes a variational principle for the topological pressure of saturated sets in non-uniform dynamical systems, extending the understanding of thermodynamic formalism to broader classes like beta-shifts and S-gap shifts.

Contribution

It introduces a conditional variational principle for saturated sets in systems with non-uniform structure, applicable to various complex symbolic systems.

Findings

Derived a variational principle for non-uniform systems

Applicable to beta-shifts and S-gap shifts

Broadens thermodynamic formalism understanding

Abstract

We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.