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Conformal Geometry and Dynamics

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A Fatou type theorem for complex map germs


Authors: Leonardo Câmara and Bruno Scárdua
Journal: Conform. Geom. Dyn. 16 (2012), 256-268
MSC (2010): Primary 32S65, 37F99; Secondary 32H50, 37F75, 37F10
DOI: https://doi.org/10.1090/S1088-4173-2012-00242-1
Published electronically: August 28, 2012
MathSciNet review: 2964678
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Abstract: In this paper we prove a Fatou type theorem for complex map germs. More precisely, we give (generic) conditions assuring the existence of parabolic curves for complex map germs tangent to the identity, in terms of existence of suitable formal separatrices. Such a map cannot have finite orbits.


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Additional Information

Leonardo Câmara
Affiliation: Departamento de Matemática - CCE, Universidade Federal do Espírito Santo, CP. 68530, Av. Fernando Ferrari 514, 29075-910 - Vitória - ES, Brazil
Email: leonardo.camara@ufes.br

Bruno Scárdua
Affiliation: Instituto de Matemática - Universidade Federal do Rio de Janeiro, CP. 68530-Rio de Janeiro-RJ, 21945-970 - Brazil
Email: scardua@im.ufrj.br

DOI: https://doi.org/10.1090/S1088-4173-2012-00242-1
Keywords: Complex diffeomorphism germ, parabolic curve, formal separatrix.
Received by editor(s): September 20, 2011
Published electronically: August 28, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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