A characterization of hyperbolic rational maps

DOI10.1007/s00222-010-0281-8zbMath1230.37052arXivmath/0703380OpenAlexW1592410163MaRDI QIDQ2430680

Lei Tan, Guizhen Cui

Publication date: 8 April 2011

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703380

zbMATH Keywords

hyperbolicityrational mapsdisconnected Julia setsThurston's characterization

Mathematics Subject Classification ID

Related Items (21)

Renormalizations and wandering Jordan curves of rational maps ⋮ A family of rational maps with buried Julia components ⋮ On McMullen-like mappings ⋮ Infinite-dimensional Thurston theory and transcendental dynamics I: infinite-legged spiders ⋮ A positive characterization of rational maps ⋮ On hyperbolic rational maps with finitely connected Fatou sets ⋮ On the core entropy of Newton maps ⋮ A characterization of hyperbolic rational maps ⋮ A decomposition theorem for Herman maps ⋮ Newton maps of complex exponential functions and parabolic surgery ⋮ Geometrically finite and semi-rational branched coverings of the two-sphere ⋮ On the cycles of components of disconnected Julia sets ⋮ Hyperbolic-parabolic deformations of rational maps ⋮ The landing of parameter rays at non-recurrent critical portraits ⋮ Topological cubic polynomials with one periodic ramification point ⋮ Combinatorial characterization of sub-hyperbolic rational maps ⋮ A characterization of postcritically minimal Newton maps of complex exponential functions ⋮ Canonical Thurston obstructions for sub-hyperbolic semi-rational branched coverings ⋮ Quasi-conformal rigidity of multicritical maps ⋮ Topological characterisation of rational maps with Siegel disks ⋮ Wandering continua for rational maps

Cites Work

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• Combinatorial characterization of sub-hyperbolic rational maps
• The iteration of cubic polynomials. II: Patterns and parapatterns
• A proof of Thurston's topological characterization of rational functions
• Combinations of complex dynamical systems
• Infinitely renormalizable quadratic polynomials, with non-locally connected Julia set
• Real laminations and the topological dynamics of complex polynomials
• On Crofoot-Sarason's conjecture for harmonic polynomials
• A characterization of hyperbolic rational maps
• Conjugacies between rational maps and extremal quasiconformal maps
• Exponential Thurston maps and limits of quadratic differentials
• On the dynamics of polynomial-like mappings
• Matings of quadratic polynomials
• The Classification of Critically Preperiodic Polynomials as Dynamical Systems
• Combining rational maps and controlling obstructions
• Frontiers in complex dynamics
• The combinatorial rigidity conjecture is false for cubic polynomials
• A Family of Cubic Rational Maps and Matings of Cubic Polynomials
• On the number of zeros of certain harmonic polynomials
• Sharp bounds for the valence of certain harmonic polynomials

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