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Bibliographic Details
Main Author: Treschev, Dmitry
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2404.07043
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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