Chaotic Dynamics of the heat semigroup on the Damek-Ricci spaces

Details Chaotic Dynamics of the heat semigroup on the Damek-Ricci spaces Chaotic Dynamics of the heat semigroup on the Damek-Ricci spaces

2011-09-09

arxiv.org/abs/1109.1976v1

Mathematics

Functional Analysis

Scientific paper

The Damek-Ricci spaces are solvable Lie groups and noncompact harmonic manifolds. The rank one Riemannian symmetric spaces of noncompact type sits inside it as a thin subclass. In this note we establish that for any Damek-Ricci space $S$, the heat semigroup generated by certain perturbation of the Laplace-Beltrami operator is {\em chaotic} on the Lorentz spaces $L^{p,q}(S)$, $2

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