Combinatorial rigidity for unicritical polynomials

DOI10.4007/annals.2009.170.303zbMath1204.37047arXivmath/0507240OpenAlexW2108598080WikidataQ56005114 ScholiaQ56005114MaRDI QIDQ731198

Jeremy Kahn, Artur Avila, Mikhail Lyubich, Wei Xiao Shen

Publication date: 2 October 2009

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507240

zbMATH Keywords

Mandelbrot setMultibrot sets, combinatorial rigidity, complex dynamicsunicritical polynomials

Mathematics Subject Classification ID

Related Items (28)

The dynamics of complex box mappings ⋮ Complex bounds for real maps ⋮ Unicritical laminations ⋮ On the Lyapunov exponent of certain \(SL (2,\mathbb R)\)-valued cocycles. II ⋮ Parapuzzle of the Multibrot set and typical dynamics of unimodal maps ⋮ Anosov-Katok constructions for quasi-periodic \(\operatorname{SL}(2, \mathbb{R})\) cocycles ⋮ Generalized fuzzy Mandelbrot and Mandelbar sets ⋮ On the metric upper density of Birkhoff sums for irrational rotations ⋮ Straightening maps for polynomials with one bounded critical orbit ⋮ Quantitative inductive estimates for Green's functions of non-self-adjoint matrices ⋮ Reducibility results for quasiperiodic cocycles with Liouvillean frequency ⋮ Laminational Models for Some Spaces of Polynomials of Any Degree ⋮ Complex WKB method (one-dimensional linear problems on the complex plane) ⋮ On the almost reducibility conjecture ⋮ Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian ⋮ Continuity of the Lyapunov exponent for analytic quasi-periodic cocycles with singularities ⋮ Resonance tongues and spectral gaps in quasi-periodic Schrödinger operators with one or more frequencies. A numerical exploration ⋮ Hyperbolic components and cubic polynomials ⋮ A KAM scheme for SL(2, \(\mathbb R\)) cocycles with Liouvillean frequencies ⋮ Combinatorial rigidity for some infinitely renormalizable unicritical polynomials ⋮ A tableau approach of the KSS nest ⋮ The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes ⋮ Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus ⋮ Rigidity and non-local connectivity of Julia sets of some quadratic polynomials ⋮ Combinatorial rigidity of unicritical maps ⋮ Quasi-conformal rigidity of multicritical maps ⋮ Proof of the Branner-Hubbard conjecture on Cantor Julia sets ⋮ Discontinuity of Straightening in Anti-holomorphic Dynamics: I

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