7 papers
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…
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…
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…
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. 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…
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…