Dynamics of the heat semigroup on symmetric spaces

Abstract

The aim of this paper is to show that the dynamics of $L^p$ heat semigroups ($p>2$) on a symmetric space of non-compact type is very different from the dynamics of the $L^p$ heat semigroups if $p\le 2$. To see this, it is shown that certain shifts of the $L^p$ heat semigroups have a chaotic behavior if $p>2$ and that such a behavior is not possible in the cases $p\le 2$. These results are compared with the corresponding situation for euclidean spaces and symmetric spaces of compact type where such a behavior is not possible.

14 pages; final version; to appear in Ergodic Theory and Dynamical Systems

References in corpus (1)

• $L^p$ spectral theory and heat dynamics of locally symmetric spaces

Cited by in corpus (1)

• Tensor products of recurrent hypercyclic semigroups