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 ϕ(x, y) = (yp/q, xq/p ). Some generalizations of the theory developed by Sibirsky for the 1: −1 resonant case to the p: −q resonant case are presented.