Hyperbolic expansivity and equilibrium states
type: Item
instance of: scholarly article
title: Hyperbolic expansivity and equilibrium states
zbMATH Open document ID: 0894.58058
author: Masatoshi Oka
published in: Southeast Asian Bulletin of Mathematics
publication date: 1998-09-07T00:00:00Z
review text: It is known that there is a unique equilibrium state for an expansive homeomorphism satisfying specification on a compact metric space and continuous functions satisfying certain growth conditions [see \textit{R. Bowen}, Math. Systems Theory 193-202 (1975; Zbl 0299.54031)]. Bowen announced that one can obtain a similar theorem for the case of real continuous flows. E. Franco discussed the analogous theorem for real flows in [\textit{E. Franco}, Am. J. Math. 99, 486-514 (1977; Zbl 0368.54014)]; however, the author of the present paper observes that there is a serious gap in the proof and that the definition of specification is misused. In this paper, the author introduces hyperbolic expansivity for real flows and gives a definition of specification, adding a supplementary condition to that by Franco. Next, he clarifies by covering the gaps in the paper of Franco the reason that Bowen's conjecture is true if the given definitions for expansivity and specification are assumed.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 1112722
zbMATH Keywords: equilibrium state
zbMATH Keywords: hyperbolic expansivity
zbMATH Keywords: real flows
zbMATH Keywords: specification
reviewed by: Neculai Papaghiuc
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1112722