Geography of the cubic connectedness locus: Intertwining surgery

DOI10.1016/S0012-9593(99)80013-5zbMath0959.37036arXivmath/9608213OpenAlexW2027290172MaRDI QIDQ4248066

Michael Yampolsky, Adam Lawrence Epstein

Publication date: 24 April 2001

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9608213

zbMATH Keywords

injectivitypolynomial dynamicsquadratic polynomialsrenormalizationpropernessfractalscubic polynomialspolynomial-like mapsasymptotic geography of the cubic connectedness locusbirenormalizable cubicsconstruction of a cubic polynomialdiscontinuity at the corner pointintertwining surgerymeasure of the residual Julia setproducts of Mandelbrot setsquasiconformal interpolationquasiconformal surgery techniquessurgical tools

Mathematics Subject Classification ID

Related Items (16)

Laminations from the Main Cubioid ⋮ Landing property of stretching rays for real cubic polynomials ⋮ Slices of the parameter space of cubic polynomials ⋮ Laminational Models for Some Spaces of Polynomials of Any Degree ⋮ Chirurgie croisée ⋮ Hyperbolic components and cubic polynomials ⋮ Dynamical generation of parameter laminations ⋮ Crossed renormalization of quadratic polynomials ⋮ Julia sets and Mandelbrot sets in Noor orbit ⋮ Combinatorics and topology of straightening maps. I: Compactness and bijectivity ⋮ Mandelbrot-like sets in dynamical systems with no critical points ⋮ Connectedness of the Arnold tongues for double standard maps ⋮ The combinatorial rigidity conjecture is false for cubic polynomials ⋮ Primitive tuning via quasiconformal surgery ⋮ Location of Siegel capture polynomials in parameter spaces ⋮ Models for spaces of dendritic polynomials

Cites Work

• The iteration of cubic polynomials. I: The global topology of parameter space
• On the dynamics of rational maps
• On the dynamics of polynomial-like mappings
• Non-accessible critical points of Cremer polynomials
• Renormalization and 3-Manifolds Which Fiber over the Circle
• Fixed points of polynomial maps. Part II. Fixed point portraits
• Homeomorphisms between limbs of the Mandelbrot set
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