Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Lomonaco, Luna"'
We prove that any degree $d$ rational map having a parabolic fixed point of multiplier $1$ with a fully invariant and simply connected immediate basin of attraction is mateable with the Hecke group $H_{d+1}$, with the mating realized by an algebraic
Externí odkaz:
http://arxiv.org/abs/2407.14780
Autor:
Bullett, Shaun, Lomonaco, Luna
We prove that there exists a homeomorphism $\chi$ between the connectedness locus $\mathcal{M}_{\Gamma}$ for the family $\mathcal{F}_a$ of $(2:2)$ holomorphic correspondences introduced by Bullett and Penrose, and the parabolic Mandelbrot set $\mathc
Externí odkaz:
http://arxiv.org/abs/2010.04273
Autor:
Lomonaco, Luna
We show that the definition of parabolic-like map can be slightly modified, by asking $\partial \Delta$ to be a quasiarc out of the parabolic fixed point, instead of the dividing arcs to be $C^1$ on $[-1,0]$ and $[0,1]$.
Externí odkaz:
http://arxiv.org/abs/2010.02046
Autor:
Bullett, Shaun, Lomonaco, Luna
Publikováno v:
In Advances in Mathematics 3 December 2022 410 Part B
This paper surveys some recent results concerning the dynamics of two families of holomorphic correspondences, namely ${\mathcal F}_a:z \to w$ defined by the relation $$\left( \frac{aw-1}{w-1} \right)^2 + \left( \frac{aw-1}{w-1} \right) \left( \frac{
Externí odkaz:
http://arxiv.org/abs/1710.03385
Autor:
Bullett, Shaun, Lomonaco, Luna
Publikováno v:
Advances in Marhematics 2022
We develop dynamical theory for the family of holomorphic correspondences $\mathcal{F}_a$ proved by the current authors to be matings between the modular group and parabolic rational maps in the Milnor slice $Per_1(1)$ (in 'Mating quadratic maps with
Externí odkaz:
http://arxiv.org/abs/1707.04764
Autor:
Bullett, Shaun, Lomonaco, Luna
In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of $(2:2)$ holomorphic correspondences $\mathcal{F}_a$: $$\left(\frac{aw-1}{w-1}\right)^2+\left(\frac{aw-1}{w-1}\right)\left(\frac{az+1}{z+1}\right) +\left(\frac{az+1}{z+1}
Externí odkaz:
http://arxiv.org/abs/1611.05257
Autor:
Lomonaco, Luna, Mukherjee, Sabyasachi
Publikováno v:
Indiana University Mathematics Journal, 67 (2018), 2089-2101
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 conformally conjugate parabolic germs, then the polynomials are affinely conjug
Externí odkaz:
http://arxiv.org/abs/1609.09465
Publikováno v:
DCDS-A Vol 37 Issue 10 (2017) pp 5085 - 5104
We prove that any $C^{1+BV}$ degree $d \geq 2$ circle covering $h$ having all periodic orbits weakly expanding, is conjugate in the same smoothness class to a metrically expanding map. We use this to connect the space of parabolic external maps (comi
Externí odkaz:
http://arxiv.org/abs/1603.01609
Publikováno v:
Invent. math. (2017) 210:615-644
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 Mandelbrot set inside the Mandelbrot set. They conjectured that in case of
Externí odkaz:
http://arxiv.org/abs/1505.05422