Periodic complex map germs and foliations

Abstract In this paper we study topological and analytical conditions on the orbits of a germ of diffeomorphism in the complex plane in order to obtain periodicity. In particular, we give a simple proof of a finiteness criteria for groups of analytic diffeomorphisms, stated in Brochero Martínez 2003. As an application, we derive some consequences about the integrability of complex vector fields in dimension three in a neighborhood of a singular point.

Infinitesimal initial part of a singular foliation

This work provides a necessary and sufficient condition to assure that two generalized curve singular foliations have the same reduction of singularities and same Camacho-Sad indices at each infinitely near point.

Este trabalho fornece uma condição necessária e suficiente a fim de que duas folheações singulares curva generalizada admitam mesma redução de singularidades e mesmo índice de Camacho-Sad em cada ponto infinitamente vizinho.