Normalization of rationally integrable systems
Dynamical Systems
2025-01-16 v2
Abstract
In two previous papers we showed that any analytically integrable vector field admits a local analytic Poincar\'e-Birkhoff normalization in the neighborhood of a singular point. The aim of this paper is to extend this analytic normalization result to the case of rationally integrable systems, where the first integrals and commuting vector fields are not required to be analytic, but just rational (i.e., quotients of analytic functions or vector fields by analytic functions).
Cite
@article{arxiv.1803.04800,
title = {Normalization of rationally integrable systems},
author = {Nguyen Tien Zung},
journal= {arXiv preprint arXiv:1803.04800},
year = {2025}
}
Comments
revised version, 15 pages, title changed