Unique equilibrium states for some intermediate beta transformations

TL;DR

This paper proves the uniqueness of equilibrium states for certain intermediate beta transformations with specific orbit properties, advancing understanding in dynamical systems and ergodic theory.

Contribution

It establishes the uniqueness of equilibrium states for a class of intermediate beta transformations with bounded orbit conditions, which was previously unresolved.

Findings

Uniqueness of equilibrium states for intermediate beta transformations with $eta > 2$.

Conditions on the orbit of 0 ensure the uniqueness.

Advances the theory of dynamical systems with non-standard beta transformations.

Abstract

We prove uniqueness of equilibrium states for subshifts corresponding to intermediate beta transformations with $\beta > 2$ having the property that the orbit of 0 is bounded away from 1.