3 citations · 5 across the 13 of their papers we have counts for
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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…