Large deviations, Gibbs measures and closed orbits for hyperbolic flows
type: Item
instance of: scholarly article
title: Large deviations, Gibbs measures and closed orbits for hyperbolic flows
zbMATH Open document ID: 0843.58102
DOI: 10.1007/BF02572611
author: Mark Pollicott
published in: Mathematische Zeitschrift
publication date: 1996-03-17T00:00:00Z
full work available at URL: https://eudml.org/doc/174806
review text: To the results of Bowen and Parry on spatial distribution of closed orbits and Gibbs measures for hyperbolic flows by large deviation type we add estimates on the exceptional closed orbits in these distribution results (Theorem 1). As a special case, we can apply these results to closed orbits of geodesic flows on compact negatively curved manifolds and the Liouville measure (Corollary 2). As an application we use these to study certain selective zeta functions whose definition involves only closed orbits which support invariant probability measures lying in a weak star closed set \({\mathcal K}\) (Theorem 2 and Proposition 5).
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
Mathematics Subject Classification ID: 37C25
zbMATH DE Number: 856561
zbMATH Keywords: large deviations
zbMATH Keywords: Gibbs measures
zbMATH Keywords: hyperbolic flows
zbMATH Keywords: closed orbits
zbMATH Keywords: geodesic flows
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 856561