Rigid reparametrizations and cohomology for horocycle flows
type: Item
instance of: scholarly article
title: Rigid reparametrizations and cohomology for horocycle flows
zbMATH Open document ID: 0697.58046
DOI: 10.1007/BF01388912
published in: Inventiones Mathematicae
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143457
review text: In a series of earlier papers the author proved various ``rigidity'' properties of the classical horocycle flow, namely the actions of the one-parameter subgroup \(\{\begin{pmatrix} 1&t \\ 0&1 \end{pmatrix}:\) \(t\in {\mathbb{R}}\}\) on homogeneous spaces of \(SL(2,{\mathbb{R}})\) with finite invariant volume, and other flows arising from them by time changes. The term rigidity refers to there being only canonical algebraic isomorphisms, factor relations, etc., between them. The present paper is a continuation of that work. It is shown that for flows obtained from horocycle flows by \(C^ 1\)-time changes all the ergodic joinings as well as their factors are algebraic. Also, nontrivial joining of two such flows is related to a certain cohomological relation between the time changes.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 28D10
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 4143109
zbMATH Keywords: rigidity
zbMATH Keywords: flows
zbMATH Keywords: horocycle flows
MaRDI profile type: Publication
cites work: Semi-rigidity of horocycle flows over compact surfaces of variable negative curvature
cites work: Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
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cites work: Q3027953
cites work: Metric Classification of Ergodic Nilflows and Unipotent Affines
cites work: Q5670852
cites work: Rigidity of horocycle flows
cites work: Factors of horocycle flows
cites work: Horocycle flows, joinings and rigidity of products
cites work: Rigidity of time changes for horocycle flows
cites work: The rate of mixing for geodesic and horocycle flows
cites work: An example of a measure preserving map with minimal self-joinings, and applications
cites work: Rigidity of some translations on homogeneous spaces
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author: Marina Ratner
description: scientific article; zbMATH DE number 4143109