Normal Forms of $C^\infty$ Vector Fields based on the Renormalization Group
Dynamical Systems
2024-06-19 v1
Abstract
The normal form theory for polynomial vector fields is extended to those for vector fields vanishing at the origin. Explicit formulas for the normal form and the near identity transformation which brings a vector field into its normal form are obtained by means of the renormalization group method. The dynamics of a given vector field such as the existence of invariant manifolds is investigated via its normal form. The normal form theory is applied to prove the existence of infinitely many periodic orbits of two dimensional systems which is not shown from polynomial normal forms.
Keywords
Cite
@article{arxiv.2009.12771,
title = {Normal Forms of $C^\infty$ Vector Fields based on the Renormalization Group},
author = {Hayato Chiba},
journal= {arXiv preprint arXiv:2009.12771},
year = {2024}
}