Dynamics of quadratic polynomials: complex bounds for real maps

DOI10.5802/aif.1598zbMath0881.58053arXivmath/9504206OpenAlexW2045958730MaRDI QIDQ1369889

Mikhail Lyubich, Michael Yampolsky

Publication date: 20 October 1997

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9504206

zbMATH Keywords

local connectivityquadratic polynomialsrenormalizationone-dimensional dynamicscomplex bounds

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Low-dimensional dynamical systems (37E99) Dynamical systems over complex numbers (37F99)

Related Items (20)

Rigidity of smooth critical circle maps ⋮ Complex a priori bounds revisited. ⋮ The dynamics of complex box mappings ⋮ Complex bounds for real maps ⋮ On analytic perturbations of a family of Feigenbaum-like equations ⋮ Lower bounds on the Hausdorff dimension of some Julia sets ⋮ No hyperbolic sets in \(J_{\infty}\) for infinitely renormalizable quadratic polynomials ⋮ Asymptotically holomorphic methods for infinitely renormalizable unimodal maps ⋮ Regular or stochastic dynamics in real analytic families of unimodal maps ⋮ Period doubling in area-preserving maps: an associated one-dimensional problem ⋮ Ergodicity of conformal measures for unimodal polynomials ⋮ CONTINUOUS EXTENSIONS ARE NOT HÖLDER ⋮ The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes ⋮ Rigidity of critical circle mappings II ⋮ Bifurcation of unimodal maps ⋮ Renormalization in one-dimensional dynamics ⋮ Primitive tuning via quasiconformal surgery ⋮ Renormalization for unimodal maps with non-integer exponents ⋮ Lebesgue measure of Feigenbaum Julia sets ⋮ Book Review: Early days in complex dynamics: a history of complex dynamics in one variable during 1906–1942

Cites Work

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• Limit sets of S-unimodal maps with zero entropy
• Distortion of S-unimodal maps
• Local connectivity of the Julia set of real polynomials
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• Measure of solenoidal attractors of unimodal maps of the segment
• Combinatorics, geometry and attractors of quasi-quadratic maps
• Measure and dimension of solenoidal attractors of one-dimensional dynamical systems
• Fixed points of composition operators. II
• On the dynamics of polynomial-like mappings
• Distortion results and invariant Cantor sets of unimodal maps
• Infinitely Renormalizable Quadratic Polynomials
• Induced expansion for quadratic polynomials
• Complex Dynamics and Renormalization (AM-135)
• Renormalization and 3-Manifolds Which Fiber over the Circle

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