In this paper we study the dynamics of germs of quasi-parabolic one-resonant biholomorphisms of C^{n+1} fixing the origin, namely, those germs whose differential at the origin has one eigenvalue 1 and the others having a one dimensional family of resonant relations. We define some invariants and give conditions which ensure the existence of attracting domains for such maps.
Dynamics of quasi-parabolic one-resonant biholomorphisms / BRACCI, FILIPPO; Rong, F.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 24:(2014), pp. 1497-1508. [10.1007/s12220-012-9382-5]
Dynamics of quasi-parabolic one-resonant biholomorphisms
BRACCI, FILIPPO;
2014
Abstract
In this paper we study the dynamics of germs of quasi-parabolic one-resonant biholomorphisms of C^{n+1} fixing the origin, namely, those germs whose differential at the origin has one eigenvalue 1 and the others having a one dimensional family of resonant relations. We define some invariants and give conditions which ensure the existence of attracting domains for such maps.
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