An Infinite-dimensional KAM Theorem with Normal Degeneracy
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909186730754048 |
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| author | Du, Jiayin Xu, Lu Li, Yong |
| author_facet | Du, Jiayin Xu, Lu Li, Yong |
| contents | In this paper, we consider a classical Hamiltonian normal form with degeneracy in normal direction. In previous results, one needs to assume that the perturbation satisfies certain non-degenerate conditions in order to remove the degeneracy in the normal form. In stead of that, we introduce a topological degree condition and a weak convexity condition, which are easy to be verified, and we prove the persistence of lower dimensional tori without any restriction on perturbation but only smallness and analyticity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_06995 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Infinite-dimensional KAM Theorem with Normal Degeneracy Du, Jiayin Xu, Lu Li, Yong Dynamical Systems In this paper, we consider a classical Hamiltonian normal form with degeneracy in normal direction. In previous results, one needs to assume that the perturbation satisfies certain non-degenerate conditions in order to remove the degeneracy in the normal form. In stead of that, we introduce a topological degree condition and a weak convexity condition, which are easy to be verified, and we prove the persistence of lower dimensional tori without any restriction on perturbation but only smallness and analyticity. |
| title | An Infinite-dimensional KAM Theorem with Normal Degeneracy |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2304.06995 |