21 citations · 155 across the 24 of their papers we have counts for
5 papers · 2 filters
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…