Chaotic Billiards by Nikolai Chernov (PDF)

Description

This book covers one of the most exciting but most difficult topics in the modern theory of dynamical systems: chaotic billiards. In physics, billiard models describe various mechanical processes, molecular dynamics, and optical phenomena. The theory of chaotic billiards has made remarkable progress in the past thirty-five years, but it remains notoriously difficult for the beginner, with main results scattered in hardly accessible research articles. This is the first and so far only book that covers all the fundamental facts about chaotic billiards in a complete and systematic manner. The book contains all the necessary definitions, full proofs of all the main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become familiar with chaotic billiards but to master the subject. The book addresses graduate students and young researchers in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian geometry, topology, and complex analysis. Some of this material is summarized in the appendices to the book.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Very well organized book.

⭐This is an excellent reference book for studying chaotic billiards. The billiard systems are very important (but not easy) models in dynamical systems with many useful applications in physics. This book gives detailed descriptions of concepts and rigorous proofs on billiards, as well as the most updated results. I feel that this book is a must-have for anyone who is interested in chaotic system, in particular billiards. It is very helpful and the book is very well written.

⭐

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