Time change rigidity for unipotent flows
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929711646507008 |
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| author | Lindenstrauss, Elon Wei, Daren |
| author_facet | Lindenstrauss, Elon Wei, Daren |
| contents | We prove a dichotomy regarding the behavior of one-parameter unipotent flows on quotients of semisimple lie groups under time change. We show that if $u^{(1)}_t$ acting on $\mathbf{G}_{1}/Γ_1$ is such a flow it satisfies exactly one of the following:
(1) The flow is loosely Kronecker, and hence measurably isomorphic after an appropriate time change to any other loosely Kronecker system.
(2) The flow exhibits the following rigid behavior: if the one-parameter unipotent flow $u^{(1)} _ t$ on $\mathbf{G}_1/Γ_1$ is measurably isomorphic after time change to another such flow $u^{(2)} _ t$ on $\mathbf{G}_2/Γ_ 2$, then $\mathbf{G}_1/Γ_1 $ is isomorphic to $\mathbf{G}_2/ Γ_2$ with the isomorphism taking $u^{(1)}_t$ to $u^{(2)}_t$ and moreover the time change is cohomologous to a trivial one up to a renormalization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08081 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time change rigidity for unipotent flows Lindenstrauss, Elon Wei, Daren Dynamical Systems We prove a dichotomy regarding the behavior of one-parameter unipotent flows on quotients of semisimple lie groups under time change. We show that if $u^{(1)}_t$ acting on $\mathbf{G}_{1}/Γ_1$ is such a flow it satisfies exactly one of the following: (1) The flow is loosely Kronecker, and hence measurably isomorphic after an appropriate time change to any other loosely Kronecker system. (2) The flow exhibits the following rigid behavior: if the one-parameter unipotent flow $u^{(1)} _ t$ on $\mathbf{G}_1/Γ_1$ is measurably isomorphic after time change to another such flow $u^{(2)} _ t$ on $\mathbf{G}_2/Γ_ 2$, then $\mathbf{G}_1/Γ_1 $ is isomorphic to $\mathbf{G}_2/ Γ_2$ with the isomorphism taking $u^{(1)}_t$ to $u^{(2)}_t$ and moreover the time change is cohomologous to a trivial one up to a renormalization. |
| title | Time change rigidity for unipotent flows |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2502.08081 |