Normalization flow in the presence of a resonance
Dynamical Systems
2024-04-11 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2404.07043,
title = {Normalization flow in the presence of a resonance},
author = {Dmitry Treschev},
journal= {arXiv preprint arXiv:2404.07043},
year = {2024}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2303.02992