Dynamical Systems on Homogeneous Spaces: 190 (Translations of Mathematical Monographs) - Hardcover

American Mathematical Society

Hardcover

ISBN 10: 0821813897 ISBN 13: 9780821813898

Publisher: American Mathematical Society, 2000

Synopsis

A homogeneous flow is a dynamical system generated by the action of a closed subgroup $H$ of a Lie group $G$ on a homogeneous space of $G$. The study of such systems is of great significance because they constitute an algebraic model for more general and more complicated systems. Also, there are abundant applications to other fields of mathematics, most notably to number theory.The present book gives an extensive survey of the subject. In the first chapter the author discusses ergodicity and mixing of homogeneous flows. The second chapter is focused on unipotent flows, for which substantial progress has been made during the last 10-15 years. The culmination of this progress was M. Ratner's celebrated proof of far-reaching conjectures of Raghunathan and Dani. The third chapter is devoted to the dynamics of nonunipotent flows. The final chapter discusses applications of homogeneous flows to number theory, mainly to the theory of Diophantine approximations. In particular, the author describes in detail the famous proof of the Oppenheim-Davenport conjecture using ergodic properties of homogeneous flows.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2000
• Language: English
• ISBN 10: 0821813897
• ISBN 13: 9780821813898
• Binding: Hardcover
• Number of pages: 243