A tableau approach of the KSS nest

Authors:
Wenjuan Peng, Weiyuan Qiu, Pascale Roesch, Lei Tan and Yongcheng Yin

Journal:
Conform. Geom. Dyn. **14** (2010), 35-67

MSC (2010):
Primary 32H50, 37F10, 37F20

DOI:
https://doi.org/10.1090/S1088-4173-10-00201-8

Published electronically:
February 18, 2010

MathSciNet review:
2600535

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Abstract | References | Similar Articles | Additional Information

Abstract: 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 KL-Lemma, 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 invented by Branner and Hubbard to deal with the complexity of the dynamics of puzzle pieces. We show, in a typical situation, how to make the combination between the KSS nest and the KL-Lemma. One consequence of this is the recently proved Branner-Hubbard conjecture. Our estimates here can be used to give an alternative proof of the rigidity property.

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Additional Information

**Wenjuan Peng**

Affiliation:
School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

Email:
wenjpeng@amss.ac.cn

**Weiyuan Qiu**

Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

Email:
wyqiu@fudan.edu.cn

**Pascale Roesch**

Affiliation:
Laboratoire Émile-Picard, Université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 9, France

Email:
roesch@math.univ-toulouse.fr

**Lei Tan**

Affiliation:
Université d’Angers, Faculté des Sciences, LAREMA, 2, Boulevard Lavoisier, 49045 Angers cedex 01, France

Email:
Lei.Tan@univ-angers.fr

**Yongcheng Yin**

Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

Email:
ycyin@fudan.edu.cn

DOI:
https://doi.org/10.1090/S1088-4173-10-00201-8

Received by editor(s):
March 6, 2009

Published electronically:
February 18, 2010

Additional Notes:
The first author is supported by China Postdoctoral Science Foundation under Grant No. 20080440270, National Natural Science Foundation of China under Grant No. 10831004 and the Doctoral Education Program Foundation of China under Grant No. 20060001003

The second author is supported by National Natural Science Foundation of China under Grants No. 10831004 and 10871047

The third author is supported by EU Research Training Network CODY, Conformal Structures and Dynamics

The fourth author is supported by National Natural Science Foundation of China under Grant No. 10831004

The fifth author is supported by the project ABC of the Agence Nationale de la Recherche Francaise

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© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.