3 citations · 6 across the 8 of their papers we have counts for
11 papers
Spectrum of the basilica group and the associated real and complex 2D dynamics
Eric Bedford, Rostislav Grigorchuk, Nguyen-Bac Dang +1
In this paper, we study the iteration over the real and complex loci of a specific rational map, found by Grigorchuk and Zuk. This two dimensional map arises as the renormalization…
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…
Equidistribution of currents under Anosov group actions
Nguyen-Bac Dang, Michael Kapovich, Mikhail Lyubich +1
We study the behavior of currents on flag-manifolds under actions of Anosov subgroups of complex semisimple Lie groups G. Given a current T of bidimension (k, k) on the full flag-m…
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…
Antiholomorphic correspondences and mating II: Shabat polynomial slices
Mikhail Lyubich, Jacob Mazor, Sabyasachi Mukherjee
We study natural one-parameter families of antiholomorphic correspondences arising from Shabat polynomials, indexed by rooted dessins d'enfants. The actions of our correspondences…
A general dynamical theory of Schwarz reflections, B-involutions, and algebraic correspondences
Yusheng Luo, Mikhail Lyubich, Sabyasachi Mukherjee
In this paper, we study matings of (anti-)polynomials and Fuchsian, reflection groups as Schwarz reflections, B-involutions or as (anti-)holomorphic correspondences, as well as the…
Mating parabolic rational maps with Hecke groups
Shaun Bullett, Luna Lomonaco, Mikhail Lyubich +1
We prove that any degree rational map having a parabolic fixed point of multiplier with a fully invariant and simply connected immediate basin of attraction is mateable wit…
Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz reflections, and correspondences
Mikhail Lyubich, Sabyasachi Mukherjee
The goal of this survey is to present intimate interactions between four branches of conformal dynamics: iterations of anti-rational maps, actions of Kleinian reflection groups, dy…
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…
David extension of circle homeomorphisms, welding, mating, and removability
Mikhail Lyubich, Sergei Merenkov, Sabyasachi Mukherjee +1
We provide a David extension result for circle homeomorphisms conjugating two dynamical systems such that parabolic periodic points go to parabolic periodic points, but hyperbolic…
Quasisymmetries of Sierpiński carpet Julia sets
Mario Bonk, Misha Lyubich, Sergei Merenkov
We prove that if is a quasisymmetric homeomorphism between Sierpiński carpets that are the Julia sets of postcritically-finite rational maps, then is the restriction of a M…