This self-contained monograph presents a unified exposition of the thermodynamic
formalism and some of its main extensions, with emphasis on the relation to dimension …

We survey a collection of results in the dimension theory of dynamical systems, with
emphasis on the study of repellers and hyperbolic sets of smooth dynamics. We discuss the …

Abstract Let ϕ: X→ R be a continuous potential associated with a symbolic dynamical
system T: X→ X over a finite alphabet. Introducing a parameter β> 0 (interpreted as the …

We effect a complete study of the thermodynamic formalism, the entropy spectrum of Birkhoff
averages, and the ergodic optimization problem for a family of parabolic horseshoes. We …

In this article we study $ r $-neutralized local entropy and derive some entropy formulas. For
an ergodic hyperbolic measure of a smooth system, we show that the $ r $-neutralized local …

Let f: X→ X be a continuous dynamical system on a compact metric space X and let: X→ Rm
be an m-dimensional continuous potential. The (generalized) rotation set Rot () is defined as …

For strongly dissipative Hénon maps at the first bifurcation parameter where the uniform
hyperbolicity is destroyed by the formation of tangencies inside the limit set, we establish a …

The objective of this book is to provide a comprehensive exposition of the main results and
main techniques of dimension theory and multifractal analysis of hyperbolic flows. This …

Measures of maximal and full dimension for smooth maps Page 1 Ergod. Th. & Dynam. Sys.,
(2024), 44, 31–49 © The Author(s), 2023. Published by Cambridge University Press. doi:10.1017/etds.2023.12 …

Let $ f $ be a diffeomorphism of a manifold preserving a hyperbolic Borel probability
measure $ μ $ having transverse intersections for almost every pair of stable and unstable …