Spectral properties of horocycle flows for compact surfaces of constant negative curvature

We consider flows, called Wu flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of Wu flows and we show that Wu flows have purely absolutely continuous spectrum in the orthocomplement...

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Autor principal:	Tiedra de Aldecoa,Rafael
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2017
Materias:	Horocycle flow Anosov flow strong mixing continuous spectrum commutator methods
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100006
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spelling	oai:scielo:S0716-091720170001000062017-02-13Spectral properties of horocycle flows for compact surfaces of constant negative curvatureTiedra de Aldecoa,Rafael Horocycle flow Anosov flow strong mixing continuous spectrum commutator methods We consider flows, called Wu flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of Wu flows and we show that Wu flows have purely absolutely continuous spectrum in the orthocomplement of the constant functions. As an application, we obtain that time changes of the classical horocycle flows for compact surfaces of constant negative curvature have purely absolutely continuous spectrum in the orthocomplement of the constant functions for time changes in a regularity class slightly less than C². This generalises recent results on time changes ofhorocycle flows.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.36 n.1 20172017-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100006en10.4067/S0716-09172017000100006
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Horocycle flow Anosov flow strong mixing continuous spectrum commutator methods
spellingShingle	Horocycle flow Anosov flow strong mixing continuous spectrum commutator methods Tiedra de Aldecoa,Rafael Spectral properties of horocycle flows for compact surfaces of constant negative curvature
description	We consider flows, called Wu flows, whose orbits are the unstable manifolds of a codimension one Anosov flow. Under some regularity assumptions, we give a short proof of the strong mixing property of Wu flows and we show that Wu flows have purely absolutely continuous spectrum in the orthocomplement of the constant functions. As an application, we obtain that time changes of the classical horocycle flows for compact surfaces of constant negative curvature have purely absolutely continuous spectrum in the orthocomplement of the constant functions for time changes in a regularity class slightly less than C². This generalises recent results on time changes ofhorocycle flows.
author	Tiedra de Aldecoa,Rafael
author_facet	Tiedra de Aldecoa,Rafael
author_sort	Tiedra de Aldecoa,Rafael
title	Spectral properties of horocycle flows for compact surfaces of constant negative curvature
title_short	Spectral properties of horocycle flows for compact surfaces of constant negative curvature
title_full	Spectral properties of horocycle flows for compact surfaces of constant negative curvature
title_fullStr	Spectral properties of horocycle flows for compact surfaces of constant negative curvature
title_full_unstemmed	Spectral properties of horocycle flows for compact surfaces of constant negative curvature
title_sort	spectral properties of horocycle flows for compact surfaces of constant negative curvature
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2017
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100006
work_keys_str_mv	AT tiedradealdecoarafael spectralpropertiesofhorocycleflowsforcompactsurfacesofconstantnegativecurvature
_version_	1718439820838043648

Spectral properties of horocycle flows for compact surfaces of constant negative curvature

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