On rigidity properties of time-changes of unipotent flows
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929426697027584 |
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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 |