Introduction to the ergodic theory of chaotic billiards (Q2781063)

This book starts with an introduction to basic measure theory (as far as needed in ergodic theory) and ergodic theory. Then Lyapunov exponents and Pesin theory are discussed. The final chapter deals with billiards. This introduction to billiards is the main part of this book.NEWLINENEWLINENEWLINEAll the concepts and main ideas presented in this book are well explained and motivated. The authors try to present some main ideas in a motivating way. Therefore sometimes technical details are avoided, and in particular some proofs are omitted.NEWLINENEWLINENEWLINEAs also an introduction to ergodic theory is given, no previous knowledge of ergodic theory (and measure theory) is required from a reader. Readers familiar with ergodic theory can start with Chapter~4 (or Chapter~3, if they do not have previous knowledge of Pesin theory). After reading this book one should be able to read research papers on billiards.NEWLINENEWLINENEWLINEThe presentation in this book is good. It can be recommended to anyone who likes to learn about billiards. Even if somebody is only interested in learning ergodic theory this book can be useful, because it requires no knowledge on measure theory and it gives a good introduction to Lyapunov exponents and Pesin theory (but here many proofs are omitted).