Geometry of Normal Forms for Dynamical Systems
Mathematical Physics
2019-01-18 v1 Dynamical Systems
math.MP
Exactly Solvable and Integrable Systems
Abstract
We discuss several aspects of the geometry of vector fields in (Poincare'-Dulac) normal form. Our discussion relies substantially on Michel theory and aims at a constructive approach to simplify the analysis of normal forms via a splitting based on the action of certain groups. The case, common in Physics, of systems enjoying an a priori symmetry is also discussed in some detail.
Keywords
Cite
@article{arxiv.1806.06360,
title = {Geometry of Normal Forms for Dynamical Systems},
author = {Giuseppe Gaeta},
journal= {arXiv preprint arXiv:1806.06360},
year = {2019}
}
Comments
35 pages; to appear in a collective book