Dynamical Systems on Homogeneous Spaces (Translations of Mathematical Monographs) - Alexander N. Starkov (2000)
ISBN 0821813897
Subject Flows (Differentiable dynamical systems); Ergodic theory; Number theory
Publisher American Mathematical Society
Publication Date June 2000
Format Hardcover (260 x 184 mm)
Language e
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.

Personal Details
Collection Status In Collection
Index 188
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Product Details
LoC Classification QA614.82.S7313 2000
Dewey 515/.352
Cover Price $100.00
No. of Pages 243