Topics in Dynamics and Ergodic Theory

This collection offers a comprehensive overview of recent advancements in ergodic theory and dynamics, featuring contributions from leading researchers in the field.

In Topics in Dynamics and Ergodic Theory, readers are introduced to a compilation of insightful survey papers authored by prominent researchers in the fields of ergodic theory, low-dimensional dynamics, and topological dynamics. The book is structured into nine comprehensive chapters, each addressing significant themes and advancements in these interconnected areas of study. The diverse topics explored within these chapters highlight the depth and breadth of current research, making it an essential resource for scholars and enthusiasts alike.

The chapters delve into various intriguing subjects, including the pivotal role of ultrafilters in ergodic theory, as well as their applications in topological dynamics and Ramsey theory. Readers will encounter discussions on the topological aspects of kneading theory and its relationship with a two-dimensional counterpart known as pruning. Additionally, the book examines the dynamics of Markov odometers, Bratteli-Vershik diagrams, and the orbit equivalence of non-singular automorphisms, offering geometric proofs of Mather's connecting and accelerating theorems.

Furthermore, Topics in Dynamics and Ergodic Theory covers recent findings in one-dimensional smooth dynamics, periodic points of nonexpansive maps, and arithmetic dynamics. It also addresses the defect of factor maps and entropy theory for actions of countable amenable groups. This collection serves as a vital reference for those interested in the latest developments in these dynamic fields, fostering a deeper understanding of complex concepts and their applications.