Centralizer Rigidity near Elements of the Weyl Chamber Flow
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917635611951104 |
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| author | Wang, Zhijing Wendy |
| author_facet | Wang, Zhijing Wendy |
| contents | In this paper, we prove centralizer rigidity near an element of the Weyl chamber flow on a semisimple Lie group. We show that a volume preserving perturbation of an element of the Weyl chamber flow on a quotient $G/Γ$ of an $\mathbb{R}$-split, simple Lie group $G$ either has centralizer of dimension $0$ or $1$, or is smoothly conjugate to an element of the Weyl chamber flow. We also acquire a general condition for the centralizer of a partially hyperbolic diffeomorphism to be a Lie group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07282 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Centralizer Rigidity near Elements of the Weyl Chamber Flow Wang, Zhijing Wendy Dynamical Systems 37C79(Primary), 37D30, 37A17 In this paper, we prove centralizer rigidity near an element of the Weyl chamber flow on a semisimple Lie group. We show that a volume preserving perturbation of an element of the Weyl chamber flow on a quotient $G/Γ$ of an $\mathbb{R}$-split, simple Lie group $G$ either has centralizer of dimension $0$ or $1$, or is smoothly conjugate to an element of the Weyl chamber flow. We also acquire a general condition for the centralizer of a partially hyperbolic diffeomorphism to be a Lie group. |
| title | Centralizer Rigidity near Elements of the Weyl Chamber Flow |
| topic | Dynamical Systems 37C79(Primary), 37D30, 37A17 |
| url | https://arxiv.org/abs/2309.07282 |