Displaying similar documents to “A parabolic Pommerenke-Levin-Yoccoz inequality”

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...

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 image of a finely holomorphic map is pluripolar

Armen Edigarian, Said El Marzguioui, Jan Wiegerinck (2010)

Annales Polonici Mathematici

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We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.

Iterations of rational functions: which hyperbolic components contain polynomials?

Feliks Przytycki (1996)

Fundamenta Mathematicae

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Let H d be the set of all rational maps of degree d ≥ 2 on the Riemann sphere, expanding on their Julia set. We prove that if f ∈ H d and all, or all but one, critical points (or values) are in the basin of immediate attraction to an attracting fixed point then there exists a polynomial in the component H(f) of H d containing f. If all critical points are in the basin of immediate attraction to an attracting fixed point or a parabolic fixed point then f restricted to the Julia set is conjugate...