Entropy in ergodic theory and topological dynamics

Manfred Einsiedler, Elon Lindenstrauss, and Thomas Ward

Entropy in Ergodic Theory
and Topological Dynamics

This is the second volume of a project that began with the volume Ergodic Theory with a view toward Number Theory by Einsiedler and Ward. This second volume aims to develop the basic machinery of measure-theoretic entropy, and topological entropy on compact spaces. This web page contains some early drafts of some of the planned chapters. Please send any comments to the authors (if possible mentioning the date of the file you are using).

Chapter 1: Measure-theoretic entropy, Introduction (February 2021)
Chapter 2: Conditional measure-theoretic entropy (February 2021)
Chapter 3: Entropy and names (February 2021)
Chapter 4: Existence of generators (November 2020)
Chapter 5: Entropy for continuous maps (November 2020)
Chapter 6: Lifting entropy (November 2020)
Chapter 8: Measures of maximal entropy (November 2020)
Chapter 9: Commuting Automorphisms (November 2020)
Hints for Selected Problems (June 2017)
Appendix A: Basic notions of ergodic theory (June 2017)
Appendix C: Adeles and local fields (June 2017)
References (March 2018)

A subsequent volume, Homogeneous dynamics and applications, will use the material of the first two volumes to develop the relationship between the ergodic theory of homogeneous spaces and applications in number theory.