5 citations · 16 across the 13 of their papers we have counts for
14 papers
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 contains infinitely many small copies of itself, each canonically homeomorphic to via the Douady--Hubbard theory of polynomial-like m…
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…
A note on parabolic-like maps
Luna Lomonaco
We show that the definition of parabolic-like map can be slightly modified, by asking to be a quasiarc out of the parabolic fixed point, instead of the dividing arcs t…
Mating quadratic maps with the modular group III: The modular Mandelbrot set
Shaun Bullett, Luna Lomonaco
We prove that there exists a homeomorphism between the connectedness locus for the family of holomorphic correspondences introduced by B…
Correspondences in complex dynamics
Shaun Bullett, Luna Lomonaco, Carlos Siqueira
This paper surveys some recent results concerning the dynamics of two families of holomorphic correspondences, namely defined by the relation $$\left( \fra…
Dynamics of Modular Matings
Shaun Bullett, Luna Lomonaco
We develop dynamical theory for the family of holomorphic correspondences proved by the current authors to be matings between the modular group and parabolic ration…
Mating quadratic maps with the modular group II
Shaun Bullett, Luna Lomonaco
In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of holomorphic correspondences : $$\left(\frac{aw-1}{w-1}\right)^2+\left(\frac{…
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…
On parabolic external maps
Luna Lomonaco, Carsten Petersen, Weixiao Shen
We prove that any degree circle covering having all periodic orbits weakly expanding, is conjugate in the same smoothness class to a metrically expanding…
On quasi-conformal (in-) compatibility of satellite copies of the Mandelbrot set: I
Luna Lomonaco, Carsten Lunde Petersen
In the paper 'On the dynamics of polynomial-like mappings' Douady and Hubbard introduced the notion of polynomial-like maps. They used it to identify homeomophic copies of the Mand…