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Tessellating the discreteness locus for the modular mating family of correspondences
Shaun Bullett, Luna Lomonaco, Arcelino Lobato do Nascimento +2
The modular Mandelbrot set , the connectedness locus of the modular mating family of 2 : 2 holomorphic correspondences on the Riemann sphere, is homeomorphic t…
Matings between compositions of rational maps and free products of finite cyclic groups
Shaun Bullett, Luna Lomonaco, Miguel Ratis Laude
Given a pair of rational maps , of degrees and , each with a parabolic fixed point having a fully invariant simply-connected basin of attraction, we construct an alg…
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 qc compatibility of satellite copies of the Mandelbrot set: II
Luna Lomonaco, Carsten Lunde Petersen
The Mandelbrot set is a fractal which classifies the behaviour of complex quadratic polynomials. Although its remarkably simple definition: $\mathcal{M}:=\{c \in \mathbb{C}\,|\,Q_c…
David regularity of the Yoccoz extension
Luna Lomonaco, Lucas Oliveira, Miguel Ratis Laude
A central problem in the study of critical circle dynamics is understanding the regularity of Yoccoz conjugators - circle homeomorphisms that conjugate critical circle maps with ir…
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…