No invariant line fields on Cantor Julia sets

DOI10.1515/FORUM.2010.004zbMath1187.37068arXivmath/0609255OpenAlexW2964148142WikidataQ122294836 ScholiaQ122294836MaRDI QIDQ5306373

Yu Zhai, Yongcheng Yin

Publication date: 9 April 2010

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0609255

zbMATH Keywords

rational mapBranner-Hubbard puzzleCantor Julia sets

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) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (17)

The dynamics of complex box mappings ⋮ Regular or stochastic dynamics in families of higher-degree unimodal maps ⋮ Moduli space of cubic Newton maps ⋮ The classification of polynomial basins of infinity ⋮ Rigidity of non-renormalizable Newton maps ⋮ On the dimensions of Cantor Julia sets of rational maps ⋮ Hyperbolic components and cubic polynomials ⋮ On the structure of Fatou domains ⋮ A tableau approach of the KSS nest ⋮ Density of hyperbolicity for rational maps with Cantor Julia sets ⋮ Rigidity for rational maps with Cantor Julia sets ⋮ Combinatorial rigidity of unicritical maps ⋮ Polynomial basins of infinity ⋮ Dynamics of McMullen maps ⋮ Quasi-conformal rigidity of multicritical maps ⋮ Proof of the Branner-Hubbard conjecture on Cantor Julia sets ⋮ On the ergodicity of conformal measures for rational maps with totally disconnected Julia sets

Cites Work

• On the instability of Herman rings
• Generic hyperbolicity in the logistic family
• Quasiconformal homeomorphisms and dynamics. III: The Teichmüller space of a holomorphic dynamical system
• The iteration of cubic polynomials. II: Patterns and parapatterns
• Dynamics of quadratic polynomials. I, II
• Rigidity for real polynomials
• Density of hyperbolicity in dimension one
• Rigidity and Expansion for Rational Maps
• Non-persistently recurrent points, qc-surgery and instability of rational maps with totally disconnected Julia sets
• Frontiers in complex dynamics
• On the measurable dynamics of real rational functions
• Remarks on the Ruelle operator and the invariant line fields problem: II

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