The Relative Variational Principle by Ledrappier and Walters: A survey

TL;DR

This survey reviews the development of the relativized variational principle in thermodynamic formalism, focusing on Ledrappier and Walters's influential 1977 work and subsequent advancements.

Contribution

It provides a comprehensive overview of the relativized variational principle, making the foundational and subsequent developments accessible to both newcomers and experts.

Findings

Summarizes key concepts of the relativized variational principle

Highlights the impact of Ledrappier and Walters's work

Discusses subsequent research developments

Abstract

Ledrappier and Walters's article "A Relativised Variational Principle for Continuous Transformations", J. Lond. Math. Soc. (2) 16 (1977), no.3, 568-576) is a landmark in the development of Thermodynamic Formalism. This survey, aimed at newcomers to the field and experts in adjacent fields discusses the background, the Ledrappier-Walters article and some subsequent developments in the field.