Time-reversibility and integrability of p:−q resonant vector fields

Abstract

We study the local analytical integrability in a neighborhood of $ p:-q $ resonant singular point of a two-dimensional vector field and its connection to time-reversibility with respect to the non-smooth involution $ \varphi(x, y) = (y^{p/q}, x^{q/p}). $ Some generalizations of the theory developed by Sibirsky for the $ 1:-1 $ resonant case to the $ p:-q $ resonant case are presented.

Keywords

• planar systems of odes
• time-reversibility
• integrability
• resonant singularity