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Dynamics of the heat semigroup on symmetric spaces

Published online by Cambridge University Press:  23 June 2009

LIZHEN JI  and
ANDREAS WEBER
LIZHEN JI
Affiliation:
Department of Mathematics, University of Michigan, 1834 East Hall, Ann Arbor, MI 48109-1043, USA (email: [email protected])
ANDREAS WEBER
Affiliation:
Institut für Algebra und Geometrie, Universität Karlsruhe (TH), Englerstrasse 2, 76128 Karlsruhe, Germany (email: [email protected])
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Abstract

The aim of this paper is to show that the dynamics of Lp heat semigroups (p>2) on a symmetric space of non-compact type is very different from the dynamics of the Lp heat semigroups if 1<p≤2. To see this, we show that certain shifts of the Lp heat semigroups have a chaotic behavior if p>2, and that such a behavior is not possible in the cases 1<p≤2. These results are compared with the corresponding situation for Euclidean spaces and symmetric spaces of compact type, where such a behavior is not possible.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 30 , Issue 2 , April 2010 , pp. 457 - 468
Copyright
Copyright © Cambridge University Press 2009

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