Normalization flow
Dynamical Systems
2023-06-27 v2
Abstract
We propose a new approach to the theory of normal forms for Hamiltonian systems near a non-resonant elliptic singular point. We consider the space of all Hamiltonian functions with such an equilibrium position at the origin and construct a differential equation in this space. Solutions of this equation move Hamiltonian functions towards their normal forms. Shifts along the flow of this equation correspond to canonical coordinate changes. So, we have a continuous normalization procedure. The formal aspect of the theory presents no difficulties. The analytic aspect and the problems of convergence of series are as usual non-trivial.
Cite
@article{arxiv.2303.02992,
title = {Normalization flow},
author = {Dmitry Treschev},
journal= {arXiv preprint arXiv:2303.02992},
year = {2023}
}
Comments
29 pages