naa a22 4500 510782167 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0035-6 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0035-6 Sarkar Rudra Stat-Math Unit, Indian Statistical Institute, 203 B. T. Rd., 700108, Calcutta, India aut Chaotic dynamics of the heat semigroup on the Damek-Ricci spaces [Elektronische Daten] [Rudra Sarkar] We consider the rank one Riemannian symmetric spaces of noncompact type and their non-symmetric generalization, namely the Damek-Ricci spaces. We show that the heat semigroup generated by a certain perturbation of the Laplace-Beltrami operator of these spaces is chaotic on their L p -spaces when p > 2. The range of p and the corresponding perturbation are sharp. A precursor to this result is due to Ji and Weber [19] where it was shown that under identical conditions the heat operator is subspace-chaotic on the Riemannian symmetric spaces, which is weaker than it being chaotic. We also extend the results to the Lorentz spaces L p,q , which are generalizations of the Lebesgue spaces. This enables us to point out that the chaoticity degenerates to subspace-chaoticity only when q = ∞. Hebrew University Magnes Press, 2013 Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 487-508 0021-2172 198:1<487 2013 198 11856 https://doi.org/10.1007/s11856-013-0035-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0035-6 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sarkar Rudra Stat-Math Unit, Indian Statistical Institute, 203 B. T. Rd., 700108, Calcutta, India aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 487-508 0021-2172 198:1<487 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer