Periodic complex map germs and foliations

2017-12-01T03:05:59Z (GMT) by LEONARDO M. CÂMARA BRUNO A. SCÁRDUA
<div><p>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.</p></div>