Denseness of intermediate pressures for systems with the Climenhaga-Thompson structures

TL;DR

This paper demonstrates that systems with Climenhaga-Thompson structures possess dense intermediate pressures and entropies, including applications to Mañé diffeomorphisms, highlighting their complex measure-theoretic properties.

Contribution

It establishes the denseness of intermediate pressures and entropies in systems with Climenhaga-Thompson structures, extending to Mañé diffeomorphisms, which was previously unproven.

Findings

Intermediate pressures are dense in these systems.

Intermediate entropies of ergodic measures are dense.

Results apply specifically to Mañé diffeomorphisms.

Abstract

We show that systems with the structure introduced by Climenhaga and Thompson have dense intermediate pressures and dense intermediate entropies of ergodic measures. The result applies to the Ma\~n\'e diffeomorphisms.