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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.07043 |
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| _version_ | 1866914747869298688 |
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| author | Treschev, Dmitry |
| author_facet | Treschev, Dmitry |
| contents | Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike arXiv:2303.02992 we do not assume that frequences of the linearized system are nonresonant. We study analytic properties of the normalization procedure. In particular we show that in the case of a codimension one resonance an analytic Hamiltonian function may be reduced to a normal form up to an exponentially small reminder with explicit estimates of the reminder and the analyticity domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Normalization flow in the presence of a resonance Treschev, Dmitry Dynamical Systems 37J40, 37J11 Following arXiv:2303.02992, we develop an approach to the Hamiltonian theory of normal forms based on continuous averaging. We concentrate on the case of normal forms near an elliptic singular point, but unlike arXiv:2303.02992 we do not assume that frequences of the linearized system are nonresonant. We study analytic properties of the normalization procedure. In particular we show that in the case of a codimension one resonance an analytic Hamiltonian function may be reduced to a normal form up to an exponentially small reminder with explicit estimates of the reminder and the analyticity domain. |
| title | Normalization flow in the presence of a resonance |
| topic | Dynamical Systems 37J40, 37J11 |
| url | https://arxiv.org/abs/2404.07043 |