{"paper":{"title":"Chaotic Dynamics of the heat semigroup on the Damek-Ricci spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rudra P Sarkar","submitted_at":"2011-09-09T12:12:01Z","abstract_excerpt":"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 $L^{p,q}(S)$, $2<p<\\infty, 1\\le q<\\infty$ and subspace-chaotic on the weak $L^p$-spaces. We show that both the amount of perturbation and the range of $p$ are sharp. This generalizes a result in \\cite{J-W} which proves that under identi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1976","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}