Analytic normalization of analytically integrable differential systems near a periodic orbit

Abstract

For an analytic differential system in ${\mathbb{R}}^n$ with a periodic orbit, we will prove that if the system is analytically integrable around the periodic orbit, i.e. it has $n-1$ functionally independent analytic first integrals defined in a neighborhood of the periodic orbit, then the system is analytically equivalent to its Poincaré--Dulac type normal form. This result is an extension for analytic integrable differential systems around a singularity to the ones around a periodic orbit.

18. Journal of Differential Equations, 2014

References in corpus (2)

• Analytic integrable systems: Analytic normalization and embedding flows
• The embedding flows of $C^{\infty }$ hyperbolic diffeomorphisms