Normalization flow in the presence of a resonance
| Autor: | Treschev, Dmitry |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: arXiv admin note: substantial text overlap with arXiv:2303.02992 |
| Databáze: | arXiv |
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