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Dynamics of the heat semigroup on symmetric spaces. (English) Zbl 1185.37077
Summary: 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 1<p2. To see this, we show 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 1<p2. These results are compared with the corresponding situation for Euclidean spaces and symmetric spaces of compact type, where such a behavior is not possible.
MSC:
37D45Strange attractors, chaotic dynamics
58J50Spectral problems; spectral geometry; scattering theory