On rigidity properties of time-changes of unipotent flows

Fuente: arXiv
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Autores principales: Artigiani, Mauro, Flaminio, Livio, Ravotti, Davide
Formato: Preprint
Publicado: 2022
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author Artigiani, Mauro
Flaminio, Livio
Ravotti, Davide
author_facet Artigiani, Mauro
Flaminio, Livio
Ravotti, Davide
contents We study time-changes of unipotent flows on finite volume quotients of semisimple linear groups, generalising previous work by Ratner on time-changes of horocycle flows. Any measurable isomorphism between time-changes of unipotent flows gives rise to a non-trivial joining supported on its graph. Under a spectral gap assumption on the groups, we show the following rigidity result: either the only limit point of this graph joining under the action of a one-parameter renormalising subgroup is the trivial joining, or the isomorphism is "affine", namely it is obtained composing an algebraic isomorphism with a (non-constant) translation along the centraliser.
format Preprint
id arxiv_https___arxiv_org_abs_2209_01253
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle On rigidity properties of time-changes of unipotent flows
Artigiani, Mauro
Flaminio, Livio
Ravotti, Davide
Dynamical Systems
37A17 (Primary) 37A20 (Secondary)
We study time-changes of unipotent flows on finite volume quotients of semisimple linear groups, generalising previous work by Ratner on time-changes of horocycle flows. Any measurable isomorphism between time-changes of unipotent flows gives rise to a non-trivial joining supported on its graph. Under a spectral gap assumption on the groups, we show the following rigidity result: either the only limit point of this graph joining under the action of a one-parameter renormalising subgroup is the trivial joining, or the isomorphism is "affine", namely it is obtained composing an algebraic isomorphism with a (non-constant) translation along the centraliser.
title On rigidity properties of time-changes of unipotent flows
topic Dynamical Systems
37A17 (Primary) 37A20 (Secondary)
url https://arxiv.org/abs/2209.01253