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Displaying similar documents to “Parabolic curves in ℂ 3 .”

Local dynamics of holomorphic diffeomorphisms

Filippo Bracci (2004)

Bollettino dell'Unione Matematica Italiana

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This is a survey about local holomorphic dynamics, from Poincaré's times to nowadays. Some new ideas on how to relate discrete dynamics to continuous dynamics are also introduced. It is the text of the talk given by the author at the XVII UMI Congress at Milano.

The dynamics of holomorphic maps near curves of fixed points

Filippo Bracci (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let M be a two-dimensional complex manifold and f : M → M a holomorphic map. Let S ⊂ M be a curve made of fixed points of f , i.e.  Fix ( f ) = S . We study the dynamics near  S in case  f acts as the identity on the normal bundle of the regular part of  S . Besides results of local nature, we prove that if  S is a globally and locally irreducible compact curve such that S · S < 0 then there exists a point p ∈ S and a holomorphic f -invariant curve with  p on the boundary which is attracted by  p under the action of  f . These results...

A topological characterization of holomorphic parabolic germs in the plane

Frédéric Le Roux (2008)

Fundamenta Mathematicae

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J.-M. Gambaudo and É. Pécou introduced the "linking property" in the study of the dynamics of germs of planar homeomorphisms in order to provide a new proof of Naishul's theorem. In this paper we prove that the negation of the Gambaudo-Pécou property characterizes the topological dynamics of holomorphic parabolic germs. As a consequence, a rotation set for germs of surface homeomorphisms around a fixed point can be defined, and it turns out to be non-trivial except for countably many...