%0 Journal Article
%T Dynamics of the heat semigroup on symmetric spaces
%A Lizhen Ji
%A Andreas Weber
%J Mathematics
%D 2008
%I arXiv
%X 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 $p\leq 2$. 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 $p\leq 2$. These results are compared with the corresponding situation for euclidean spaces and symmetric spaces of compact type where such a behavior is not possible.
%U http://arxiv.org/abs/0809.5282v2