Absence of line fields and Mañé’s theorem for nonrecurrent transcendental functions

DOI10.1090/S0002-9947-2010-05125-6zbMath1230.37056arXiv0802.0666OpenAlexW2012482386MaRDI QIDQ3082353

Sebastian J. van Strien, Lasse Rempe-Gillen

Publication date: 10 March 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0802.0666

zbMATH Keywords

invariant line fieldspostsingular setMañé's theoremnonrecurrent function

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) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (13)

The dynamics of complex box mappings ⋮ Complex bounds for real maps ⋮ Singular values and bounded Siegel disks ⋮ Rigidity of escaping dynamics for transcendental entire functions ⋮ Speiser meets Misiurewicz ⋮ A landing theorem for entire functions with bounded post-singular sets ⋮ Repelling periodic points and landing of rays for post-singularly bounded exponential maps ⋮ Rigidity and absence of line fields for meromorphic and Ahlfors islands maps ⋮ A note on hyperbolic leaves and wild laminations of rational functions ⋮ Misiurewicz parameters in the exponential family ⋮ Hyperbolic dimension and radial Julia sets of transcendental functions ⋮ On the Hausdorff dimension of the escaping set of certain meromorphic functions ⋮ Density of hyperbolicity for classes of real transcendental entire functions and circle maps

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