3 citations · 5 across the 13 of their papers we have counts for
14 papers
Combining cusped triangle groups with Blaschke products: commensurable matings
Yusheng Luo, Mahan Mj, Sabyasachi Mukherjee
In this note, we construct algebraic correspondences as matings of Fuchsian -triangle groups with Blaschke products. Combined with the results of [MM25], this proves…
Transcendental correspondences: when Fuchsian groups take over basins of entire maps
Kostiantyn Drach, Sabyasachi Mukherjee, Leticia Pardo-Simón
In this paper, we initiate a systematic study of holomorphic correspondences that naturally arise as conformal combinations (matings) of transcendental entire m…
Universality of the Basilica
Yusheng Luo, Mahan Mj, Sabyasachi Mukherjee
We establish universality of the fat Basilica Julia set in conformal dynamics in the following sense: is quasiconformally equivalent to the fat Ba…
Algebraic correspondences and Schwarz reflections: Where rational dynamics meets Kleinian groups
Luna Lomonaco, Sabyasachi Mukherjee
We present an overview of the rapidly evolving field of dynamics of algebraic correspondences, with a focus on matings between rational maps and Kleinian groups. These corresponden…
On topology and singularities of quadrature domains
Rashmita, Sabyasachi Mukherjee
We prove a linear upper bound for the number of singular points on the boundary of a quadrature domain, improving a previously known quadratic bound due to Gustafsson \cite{Gus88}.…
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…
Correspondences on hyperelliptic surfaces, combination theorems, and Hurwitz spaces
Sabyasachi Mukherjee, S. Viswanathan
We construct a general class of holomorphic correspondences of equal bi-degree on compact Riemann surfaces of arbitrary genus exhibiting rich dynamical behavior. These corresponden…
Uniformization of tongues in Double Standard Map family and variation of maximal chaotic sets
Kuntal Banerjee, Anubrato Bhattacharyya, Sabyasachi Mukherjee
We study hyperbolic components, also known as tongues, in the Double Standard Map family comprising circle maps of the form: \begin{align*} f_{a,b}(x)=\left(2x+a+\dfrac{b}π \sin(2π…
Teichmüller spaces, polynomial loci, and degeneration in spaces of algebraic correspondences
Yusheng Luo, Mahan Mj, Sabyasachi Mukherjee
We develop an analog of the notion of a character variety in the context of algebraic correspondences. It turns out that matings of certain Fuchsian groups and polynomials are cont…
Simultaneous Uniformization and Algebraic Correspondences
Mahan Mj, Sabyasachi Mukherjee
We prove a generalization of Bers' simultaneous uniformization theorem in the world of algebraic correspondences. More precisely, we construct algebraic correspondences that simult…
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…
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…