Rational maps with smooth degenerate Herman rings

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) Combinatorics and topology in relation with holomorphic dynamical systems (37F20) Quasiconformal methods in holomorphic dynamics; quasiconformal dynamics (37F31)

Cites Work

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Typical orbits of quadratic polynomials with a neutral fixed point: Brjuno type
Quadratic Julia sets with positive area
Siegel disks with smooth boundaries
Invariant analytic curves for entire functions
Riemann's mapping theorem for variable metrics
A proof of the Marmi-Moussa-Yoccoz conjecture for rotation numbers of high type
Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
Self-similarity of Siegel disks and Hausdorff dimension of Julia sets
A proof of Thurston's topological characterization of rational functions
Local connectivity of some Julia sets containing a circle with an irrational rotation
Statistical properties of quadratic polynomials with a neutral fixed point
On the Julia set of a typical quadratic polynomial with a Siegel disk
The buried points on the Julia sets of rational and entire functions
Lebesgue measure of Feigenbaum Julia sets
On the formulas of meromorphic functions with periodic Herman rings
Area and Hausdorff dimension of Sierpiński carpet Julia sets
On the Grunsky inequalities for univalent functions
Iteration of analytic functions
Invariant curves and semiconjugacies of rational functions
Smooth Siegel disks everywhere
How regular can the boundary of a quadratic Siegel disk be?
Smooth Siegel disks without number theory
On the dynamics of polynomial-like mappings
On the quasiconformal surgery of rational functions
The components of a Julia set
Complex bounds for renormalization of critical circle maps
Antipode preserving cubic maps: the Fjord theorem
Typical orbits of quadratic polynomials with a neutral fixed point: Non-Brjuno type
Quasiconformal Surgery in Holomorphic Dynamics
Dynamics in One Complex Variable. (AM-160)
HERMAN RINGS AND ARNOLD DISKS
Sur les équations fonctionnelles.
Local connectivity of the Mandelbrot set at some satellite parameters of bounded type

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