Articles liés à Dynamical Systems on Homogeneous Spaces (190)

Dynamical Systems on Homogeneous Spaces (190) - Couverture rigide

American Mathematical Society

 
9780821813898: Dynamical Systems on Homogeneous Spaces (190)
Couverture rigide
ISBN 10 : 0821813897 ISBN 13 : 9780821813898
Editeur : 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2000
Langue
anglais
ISBN 10 
0821813897
ISBN 13 
9780821813898
Reliure
Relié
Nombre de pages
243
Coordonnées du fabricant
non disponible
Personne responsable
non disponible