%0 Generic %A CÂMARA, LEONARDO M. %A SCÁRDUA, BRUNO A. %D 2017 %T Periodic complex map germs and foliations %U https://scielo.figshare.com/articles/dataset/Periodic_complex_map_germs_and_foliations/5720461 %R 10.6084/m9.figshare.5720461.v1 %2 https://ndownloader.figshare.com/files/10051120 %2 https://ndownloader.figshare.com/files/10051126 %2 https://ndownloader.figshare.com/files/10051138 %K Complex germs of diffeomorphims %K singular holomorphic foliations %K integrability of vector fields %K closed orbits %X

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.

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