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pro vyhledávání: '"Cui, Guizhen"'
In this paper, we prove that for any post-critically finite rational map $f$ on the Riemann sphere $\overline{\mathbb{C}}$, and for each sufficiently large integer $n$, there exists a finite and connected graph $G$ in the Julia set of $f$ such that $
Externí odkaz:
http://arxiv.org/abs/2408.12371
Autor:
Cui, Guizhen, Peng, Wenjuan
We give a concrete description for the boundary of the central quadratic hyperbolic component. The connectedness of the Julia sets of the boundary maps are also considered.
Comment: 9 pages,3 figures
Comment: 9 pages,3 figures
Externí odkaz:
http://arxiv.org/abs/2401.02074
A completely stable multicurve of a post-critically finite rational map induces a combinatorial decomposition. The projections of the small Julia sets are immersed within the original Julia set. We prove that two small Julia sets are disjoint if and
Externí odkaz:
http://arxiv.org/abs/2309.03464
We prove that every wandering Julia component of cubic rational maps eventually has at most two complementary components.
Comment: 10 pages, 2 figures
Comment: 10 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2308.15125
Akademický článek
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Let $f$ be a postcritically finite rational map. We prove that, as $n$ large enough, there exists an $f^n$-invariant (finite connected) graph on $\widehat{\mathbb{C}}$ such that it contains the postcritical set of $f$.
Comment: 41 pages, 7 figur
Comment: 41 pages, 7 figur
Externí odkaz:
http://arxiv.org/abs/1907.02870
Autor:
Cui, Guizhen, Peng, Wenjuan
For any integers $d\ge 3$ and $n\ge 1$, we construct a hyperbolic rational map of degree $d$ such that it has $n$ cycles of the connected components of its Julia set except single points and Jordan curves.
Comment: 30 pages, 9 figures
Comment: 30 pages, 9 figures
Externí odkaz:
http://arxiv.org/abs/1904.04541
Publikováno v:
In Advances in Mathematics 6 August 2022 404 Part B
Autor:
Arfeux, Matthieu, Cui, Guizhen
We construct a family of rational map sequences providing an arbitrary large number of dynamically independent rescaling limits of non monomial type. From this, we deduce the existence of a family of rational maps providing a non trivial dynamics on
Externí odkaz:
http://arxiv.org/abs/1606.09574
We study necessary and sufficient conditions for a meromorphic quadratic differential with prescribed poles to be the Schwarzian derivative of a rational map. We give geometric interpretations of these conditions. We also study the pole-dependency of
Externí odkaz:
http://arxiv.org/abs/1511.04246