Entropy and its variational principle for noncompact metric spaces

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dc.creatorPatrão, Mauro
dc.date2008-04-26
dc.date.accessioned2026-07-07T09:35:31Z
dc.date.available2026-07-07T09:35:31Z
dc.descriptionIn the present paper, we introduce a natural extension of AKM-topological entropy for noncompact spaces and prove a variational principle which states that the topological entropy, the supremum of the measure theoretical entropies and the minimum of the metric theoretical entropies always coincide. We apply the variational principle to show that the topological entropy of automorphisms of simply connected nilpotent Lie groups always vanishes. This shows that the classical formula for the entropy of an automorphism of a noncompact Lie group is just an upper bound for its topological entropy.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/0804.4244
dc.identifierhttp://arxiv.org/abs/0804.4244
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159856
dc.subjectDynamical Systems
dc.subjectGeneral Topology
dc.subject37B40 (Primary); 37A35, 22E25 (Secondary)
dc.titleEntropy and its variational principle for noncompact metric spaces
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