10 citations · 25 across the 14 of their papers we have counts for
19 papers
Rigidity of the attractor of neutral renormalization
Dzmitry Dudko, Willie Rush Lim, Mikhail Lyubich
We prove combinatorial rigidity for the full renormalization attractor of neutral quadratic polynomials. More precisely, any two bi-infinite renormalization towers with the same co…
Uniform bounds for bubbles of neutral quadratic polynomials
Dzmitry Dudko, Willie Rush Lim
Given a quadratic polynomial with an irrationally indifferent fixed point of bounded type, a bubble is an iterated preimage of its Siegel disk. Similar to pseudo-Siegel disks, one…
On the MLC Conjecture and the Renormalization Theory in Complex Dynamics
Dzmitry Dudko
In this Note, we present recent developments in the Renormalization Theory of quadratic polynomials and discuss their applications, with an emphasis on the MLC conjecture, the prob…
Uniform a priori bounds for neutral renormalization. Variation II: -ql Siegel maps
Dzmitry Dudko, Yusheng Luo, Mikhail Lyubich
We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to -quadratic-like Siegel maps. In this form, the bounds are compatible with the -quadratic-l…
Correspondences on Riemann surfaces and non-uniform hyperbolicity
Laurent Bartholdi, Dzmitry Dudko, Kevin M. Pilgrim
We consider certain correspondences on a Riemann surface, and show that they admit a weak form of hyperbolicity: sufficiently long loops get shorter under lifting at a fixed point…
MLC at Feigenbaum points
Dzmitry Dudko, Mikhail Lyubich
We prove a priori bounds for Feigenbaum quadratic polynomials, i.e., infinitely renormalizable polynomials of bounded type. It implies local connectivity of t…
Uniform a priori bounds for neutral renormalization
Dzmitry Dudko, Mikhail Lyubich
We prove uniform ``pseudo-Siegel'' a priori bounds for Siegel disks of bounded type that give a uniform control of oscillations of their boundaries in all scales. As a consequence,…
A canonical decomposition of postcritically finite rational maps and their maximal expanding quotients
Dzmitry Dudko, Mikhail Hlushchanka, Dierk Schleicher
We provide a natural canonical decomposition of postcritically finite rational maps with non-empty Fatou sets based on the topological structure of their Julia sets. The building b…
Local connectivity of the Mandelbrot set at some satellite parameters of bounded type
Dzmitry Dudko, Mikhail Lyubich
We explore geometric properties of the Mandelbrot set M, and the corresponding Julia sets J_c, near the main cardioid. Namely, we establish that: a) M is locally connected at certa…
Algorithmic aspects of branched coverings III/V. Erasing maps, orbispaces, and the Birman exact sequence
Laurent Bartholdi, Dzmitry Dudko
Let be a Thurston map and let be its mapping class biset: isotopy classes rel of maps obtained by pre- and…
Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters
Dzmitry Dudko, Mikhail Lyubich, Nikita Selinger
In the 1980s Branner and Douady discovered a surgery relating various limbs of the Mandelbrot set. We put this surgery in the framework of "Pacman Renormalization Theory" that comb…
Algorithmic aspects of branched coverings IV/V. Expanding maps
Laurent Bartholdi, Dzmitry Dudko
Thurston maps are branched self-coverings of the sphere whose critical points have finite forward orbits. We give combinatorial and algebraic characterizations of Thurston maps tha…
Algorithmic aspects of branched coverings II/V. Sphere bisets and their decompositions
Laurent Bartholdi, Dzmitry Dudko
We consider "Thurston maps": branched self-coverings of the sphere with ultimately periodic critical points, and prove that the Thurston equivalence problem between them (continuou…
Algorithmic aspects of branched coverings I. Van Kampen's Theorem for bisets
Laurent Bartholdi, Dzmitry Dudko
We develop a general theory of "bisets": sets with two commuting group actions. They naturally encode topological correspondences. Just as van Kampen's theorem decomposes into a gr…
Algorithmic aspects of branched coverings
Laurent Bartholdi, Dzmitry Dudko
This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-th…
Core entropy of quadratic polymonials
Dzmitry Dudko, Dierk Schleicher
We give a combinatorial definition of "core entropy" for quadratic polynomials as the growth exponent of the number of certain precritical points in the Julia set (those that separ…
Matings with laminations
Dzmitry Dudko
We give a topological description of the space of quadratic rational maps with superattractive two-cycles: its "non-escape locus" M2 (the analog of the Mandelbrot set M) is locally…
Homeomorphisms between limbs of the Mandelbrot set
Dzmitry Dudko, Dierk Schleicher
We prove that for every hyperbolic component of the Mandelbrot set, any two limbs with equal denominators are homeomorphic so that the homeomorphism preserves periods of hyperbolic…
The Decoration Theorem for Mandelbrot and Multibrot Sets
Dzmitry Dudko
We prove the decoration theorem for the Mandelbrot set (and Multibrot sets) which says that when a "little Mandelbrot set" is removed from the Mandelbrot set, then most of the resu…