We discuss several aspects of the geometry of vector fields in (Poincar´e-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.
Geometry of Normal Forms for Dynamical Systems / G. Gaeta - In: Nonlinear Systems and Their Remarkable Mathematical Structures. 1 / [a cura di] N. Euler. - Prima edizione. - [s.l] : CRC Press, 2018. - ISBN 9781138601000. - pp. 352-389
Geometry of Normal Forms for Dynamical Systems
G. Gaeta
2018
Abstract
We discuss several aspects of the geometry of vector fields in (Poincar´e-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.
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