199 citations · 525 across the 46 of their papers we have counts for
53 papers
Structure of hyperbolic polynomial automorphisms of C^2 with disconnected Julia sets
Romain Dujardin, Mikhail Lyubich
For a hyperbolic polynomial automorphism of C^2 with a disconnected Julia set, and under a mild dissipativity condition, we give a topological description of the components of the…
Antiholomorphic correspondences and mating I: realization theorems
Mikhail Lyubich, Jacob Mazor, Sabyasachi Mukherjee
In this paper, we bring together four different branches of antiholomorphic dynamics: of global anti-rational maps, reflection groups, Schwarz reflections in quadrature domains, an…
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,…
The Critical Locus and Rigidity of Foliations of Complex Henon Maps
Misha Lyubich, John W. Robertson
We study Henon maps which are perturbations of a hyperbolic polynomial p with connected Julia set. We give a complete description of the critical locus of these maps. In particular…
Self-similar groups and holomorphic dynamics: Renormalization, integrability, and spectrum
Nguyen-Bac Dang, Rostislav Grigorchuk, Mikhail Lyubich
In this paper, we explore the spectral measures of the Laplacian on Schreier graphs for several self-similar groups (the Grigorchuk, Lamplighter, and Hanoi groups) from the dynamic…
On Dynamical Gaskets Generated by Rational Maps, Kleinian Groups, and Schwarz Reflections
Russell Lodge, Mikhail Lyubich, Sergei Merenkov +1
According to the Circle Packing Theorem, any triangulation of the Riemann sphere can be realized as a nerve of a circle packing. Reflections in the dual circles generate a Kleinian…