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- Weiyuan Qiu, Yongcheng Yin
- 2006

By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove that the Julia set of a polynomial is a Cantor set if and only if each component of the filled-in Julia set containing critical points is aperiodic. This result was a conjecture… (More)

- WENJUAN PENG, WEIYUAN QIU, PASCALE ROESCH, LEI TAN, YONGCHENG YIN
- 2010

The KSS nest is a sophisticated choice of puzzle pieces given in [Ann. of Math. 165 (2007), 749–841]. This nest, once combined with the KLLemma, has proven to be a powerful machinery, leading to several important advancements in the field of holomorphic dynamics. We give here a presentation of the KSS nest in terms of tableau. This is an effective language… (More)

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to the question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that… (More)

- Yeshun Sun, Yongcheng Yin
- I. J. Bifurcation and Chaos
- 2007

- WEIYUAN QIU, PASCALE ROESCH, XIAOGUANG WANG, YONGCHENG YIN
- 2012

In this article, we study the hyperbolic components of Mc-Mullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the boundary of the unbounded hyperbolic component. This is a dynamical analogue of McMullen's theorem that cusps are… (More)

- FENG XIE, YONGCHENG YIN, YESHUN SUN
- 2003

Let f i (x) = A i x + b i (1 ≤ i ≤ n) be affine maps of Euclidean space R N with each A i nonsingular and each f i contractive. We prove that the self-affine set K of {f 1 ,. .. , fn} is uniformly perfect if it is not a singleton.

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