Margulis distributions for Anosov flows
type: Item
instance of: scholarly article
title: Margulis distributions for Anosov flows
zbMATH Open document ID: 0633.58037
DOI: 10.1007/BF01221402
author: Mark Pollicott
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: \textit{G. A. Margulis} [Funct. Anal. Appl. 4, 55-67 (1970), translation from Funkts. Anal. Prilozh. 4, No.1, 62-76 (1970; Zbl 0245.58003)] constructed a (unique) transverse measure for the strong-stable foliation of an Anosov flow. In this paper Margulis' result is extended to more general ``transverse distributions'' for the foliation. As an application the author derives his main result to the effect that the nonzero analytic extension to a strip of the Selberg zeta function for compact surfaces of constant negative curvature persists under small perturbations in the metric. He also states an equivalent formulation in terms of the Fourier transform of the correlation function.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 42A38
Mathematics Subject Classification ID: 58C35
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 4030566
zbMATH Keywords: Margulis measure
zbMATH Keywords: strong-stable foliation
zbMATH Keywords: axiom A flow
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: transverse measure
zbMATH Keywords: Anosov flow
zbMATH Keywords: Selberg zeta function
reviewed by: Dušan Repovš
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4030566