A Fatou Type Theorem for Complex Map Germs
نویسنده
چکیده
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.
منابع مشابه
The dynamics of holomorphic germs near a curve of fixed points
One of the interesting areas in the study of the local dynamics in several complex variables is the dynamics near the origin O of maps tangent to the identity, that is of germs of holomorphic self-maps f : n → n such that f (O) = O and d fO = id. When n = 1 the dynamics is described by the known Leau–Fatou flower theorem but when n > 1, we are still far from understanding the complete picture, ...
متن کاملHolomorphic Motions, Fatou Linearization, and Quasiconformal Rigidity for Parabolic Germs
By applying holomorphic motions, we prove that a parabolic germ is quasiconformal rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near conformal as long as we consider these germs defined on smaller and smaller neighborhoods. Before to prove this theorem, we use the idea of holomorphic motions to ...
متن کاملClassification and Structure of Periodic Fatou Components
For a given rational map f : Ĉ→ Ĉ, the Julia set consists of those points in Ĉ around which the dynamics of the map is chaotic (a notion that can be defined rigorously), while the Fatou set is defined as the complement. The Fatou set, where the dynamics is well-behaved, is an open set, and one can classify its periodic connected components into five well-understood categories. This classificati...
متن کاملClassification of Invariant Fatou Components for Dissipative Hénon Maps
Fatou components for rational functions in the Riemann sphere are very well understood and play an important role in our understanding of one-dimensional dynamics. In higher dimensions the situation is less well understood. In this work we give a classification of invariant Fatou components for moderately dissipative Hénon maps. Most of our methods apply in a much more general setting. In parti...
متن کاملar X iv : 0 80 2 . 21 11 v 1 [ m at h . C V ] 1 4 Fe b 20 08 HOLOMORPHIC MOTIONS AND RELATED TOPICS
In this article we give an expository account of the holomorphic motion theorem based on work of Mãne-Sad-Sullivan, Bers-Royden, and Chirka. After proving this theorem, we show that tangent vectors to holomorphic motions have |ǫ log ǫ| moduli of continuity and then show how this type of continuity for tangent vectors can be combined with Schwarz’s lemma and integration over the holomorphic vari...
متن کامل