Siegel disks with critical points in their boundaries

DOI10.1215/S0012-7094-03-11916-XzbMath1037.37022OpenAlexW1965667804MaRDI QIDQ1409337

Jacek Graczyk, Grzegorz Świątek

Publication date: 13 October 2003

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-03-11916-x

zbMATH Keywords

critical pointrotation numberSiegel disk

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Polynomials and rational functions of one complex variable (30C10) Rotation numbers and vectors (37E45)

Related Items (16)

Herman's condition and Siegel disks of bi-critical polynomials ⋮ Quadratic rational maps with a 2-cycle of Siegel disks ⋮ On the dynamics of a family of entire functions ⋮ Singular values and bounded Siegel disks ⋮ Arithmetic geometric model for the renormalisation of irrationally indifferent attractors ⋮ Rational maps without Herman rings ⋮ Combination laws for scaling exponents and relation to the geometry of renormalization operators ⋮ A decomposition theorem for Herman maps ⋮ Bounded type Siegel disks of finite type maps with few singular values ⋮ On Siegel disks of a class of entire maps ⋮ Bounded-type Siegel disks of a one-dimensional family of entire functions ⋮ Numerical computation of the asymptotic size of the rotation domain for the Arnold family ⋮ Siegel disks of the tangent family ⋮ Bounded type Siegel disks of a family of sine families ⋮ Boundaries of Siegel disks: Numerical studies of their dynamics and regularity ⋮ Some transcendental entire functions with irrationally indifferent fixed points

Cites Work

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• Are there critical points on the boundaries of singular domains?
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Iteration of analytic functions
• A Uniqueness Theorem for Beltrami Equations

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