21 citations · 155 across the 24 of their papers we have counts for
20 papers · 1 filter
Matings, holomorphic correspondences, and a Bers slice
Mahan Mj, Sabyasachi Mukherjee
There are two frameworks for mating Kleinian groups with rational maps on the Riemann sphere: the algebraic correspondence framework due to Bullett-Penrose-Lomonaco \cite{BP94,BL20…
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…
The Sullivan dictionary and Bowen-Series maps
Mahan Mj, Sabyasachi Mukherjee
The Sullivan dictionary between Kleinian groups and rational dynamics describes striking similarities between the fields, both in terms of the objects of study as well as the techn…
On Deformation Space Analogies between Kleinian Reflection Groups and Antiholomorphic Rational Maps
Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
In a previous paper, we constructed an explicit dynamical correspondence between certain Kleinian reflection groups and certain anti-holomorphic rational maps on the Riemann sphere…
Combining Rational maps and Kleinian groups via orbit equivalence
Mahan Mj, Sabyasachi Mukherjee
We develop a new orbit equivalence framework for holomorphically mating the dynamics of complex polynomials with that of Kleinian surface groups. We show that the only torsion-free…
Discontinuity of straightening in anti-holomorphic dynamics: II
Hiroyuki Inou, Sabyasachi Mukherjee
In [M3], Milnor found Tricorn-like sets in the parameter space of real cubic polynomials. We give a rigorous definition of these Tricorn-like sets as suitable renormalization loci,…
Circle packings, kissing reflection groups and critically fixed anti-rational maps
Russell Lodge, Yusheng Luo, Sabyasachi Mukherjee
In this paper, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simpl…
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…
Schwarz reflections and anti-holomorphic correspondences
Seung-Yeop Lee, Mikhail Lyubich, Nikolai G. Makarov +1
In this paper, we continue exploration of the dynamical and parameter planes of one-parameter families of Schwarz reflections that was initiated in \cite{LLMM1,LLMM2}. Namely, we c…
Schwarz reflections and the Tricorn
Seung-Yeop Lee, Mikhail Lyubich, Nikolai G. Makarov +1
We continue our exploration of the family of Schwarz reflection maps with respect to the cardioid and a circle which was initiated in our earlier work. We prove that…
Dynamics of Schwarz reflections: the mating phenomena
Seung-Yeop Lee, Mikhail Lyubich, Nikolai G. Makarov +1
We initiate the exploration of a new class of anti-holomorphic dynamical systems generated by Schwarz reflection maps associated with quadrature domains. More precisely, we study S…
On The Support of The Bifurcation Measure of Cubic Polynomials
Hiroyuki Inou, Sabyasachi Mukherjee
We construct new examples of cubic polynomials with a parabolic fixed point that cannot be approximated by Misiurewicz polynomials. In particular, such parameters admit maximal bif…
Invisible Tricorns in Real Slices of Rational Maps
Russell Lodge, Sabyasachi Mukherjee
One of the conspicuous features of real slices of bicritical rational maps is the existence of Tricorn-type hyperbolic components. Such a hyperbolic component is called invisible i…
Antiholomorphic perturbations of Weierstrass Zeta functions and Green's function on tori
Konstantin Bogdanov, Khudoyor Mamayusupov, Sabyasachi Mukherjee +1
In \cite{BeEr}, Bergweiler and Eremenko computed the number of critical points of the Green's function on a torus by investigating the dynamics of a certain family of antiholomorph…
A rigidity result for some parabolic germs
Luna Lomonaco, Sabyasachi Mukherjee
The goal of this article is to prove a rigidity result for unicritical polynomials with parabolic cycles. More precisely, we show that if two unicritical polynomials have conformal…
Rational Parameter Rays of The Multibrot Sets
Dominik Eberlein, Sabyasachi Mukherjee, Dierk Schleicher
We prove a structure theorem for the multibrot sets, which are the higher degree analogues of the Mandelbrot set, and give a complete picture of the landing behavior of the rationa…
Parabolic arcs of the multicorns: Real-analyticity of Hausdorff dimension, and singularities of curves
Sabyasachi Mukherjee
The boundaries of the hyperbolic components of odd period of the multicorns contain real-analytic arcs consisting of quasi-conformally conjugate parabolic parameters. One of the ma…
Non-landing parameter rays of the multicorns
Hiroyuki Inou, Sabyasachi Mukherjee
It is well known that every rational parameter ray of the Mandelbrot set lands at a single parameter. We study the rational parameter rays of the multicorn , the c…
Orbit Portraits of Unicritical Anti-polynomials
Sabyasachi Mukherjee
Orbit portraits were introduced by Milnor as a combinatorial tool to describe the patterns of all periodic dynamical rays landing on a periodic cycle of a quadratic polynomial. Thi…
On Multicorns and Unicorns II: Bifurcations in Spaces of Antiholomorphic Polynomials
Sabyasachi Mukherjee, Shizuo Nakane, Dierk Schleicher
The multicorns are the connectedness loci of unicritical antiholomorphic polynomials . We investigate the structure of boundaries of hyperbolic components: we prove…