Infinitely renormalizable quadratic polynomials, with non-locally connected Julia set

DOI10.1007/BF02921810zbMath0984.37047WikidataQ121611739 ScholiaQ121611739MaRDI QIDQ1589314

Dan Erik Krarup Sørensen

Publication date: 11 December 2000

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

satelliterobustnessquadratic polynomialJulia setlocal connectivitywakeMandelbrot settuningexternal rayaccumulation setinfinitely renormalizableprime endhyperbolic componentsimpression

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) 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) Renormalization of holomorphic dynamical systems (37F25)

Related Items

Multipliers of periodic orbits of quadratic polynomials and the parameter plane, No hyperbolic sets in \(J_{\infty}\) for infinitely renormalizable quadratic polynomials, Asymptotically holomorphic methods for infinitely renormalizable unimodal maps, A characterization of hyperbolic rational maps, Rigidity and non-local connectivity of Julia sets of some quadratic polynomials, The combinatorial rigidity conjecture is false for cubic polynomials, Hairy Cantor sets

Cites Work

• On the dynamics of polynomial-like mappings
• Building blocks for quadratic Julia sets
• Describing quadratic Cremer point polynomials by parabolic perturbations
• Accumulation theorems for quadratic polynomials
• Disconnected Julia set and rotation sets
• Fixed points of polynomial maps. Part II. Fixed point portraits
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