Hyperbolic entire functions with bounded Fatou components

DOI10.4171/CMH/371zbMath1338.37056arXiv1404.0925MaRDI QIDQ906564

Walter Bergweiler, Lasse Rempe-Gillen, Núria Fagella

Publication date: 22 January 2016

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.0925

zbMATH Keywords

locally connectedhyperbolic mapsquasidiscs

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (18)

Fatou's associates ⋮ A class of Newton maps with Julia sets of Lebesgue measure zero ⋮ Hausdorff dimension of escaping sets of meromorphic functions II ⋮ Orbifold expansion and entire functions with bounded Fatou components ⋮ Hyperbolic entire functions and the Eremenko-Lyubich class: Class \(\mathcal {B}\) or not class \(\mathcal {B}\)? ⋮ Models for the Eremenko–Lyubich class ⋮ Geometrically finite transcendental entire functions ⋮ Speiser meets Misiurewicz ⋮ Entire functions arising from trees ⋮ Results on escaping set of an entire function and its composition ⋮ Constructing entire functions with non-locally connected Julia set by quasiconformal surgery ⋮ Dynamics of two parameter family of hyperbolic sine like functions ⋮ Dynamics in the Eremenko-Lyubich class ⋮ Lebesgue measure of escaping sets of entire functions ⋮ Fixed points and dynamics of two-parameter family of hyperbolic cosine like functions ⋮ Singularities of inner functions associated with hyperbolic maps ⋮ On connected preimages of simply-connected domains under entire functions ⋮ Accesses to infinity from Fatou components

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