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

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 nonsmooth involution (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. [ABSTRACT FROM AUTHOR]