A tableau approach of the KSS nest

Peng, Wenjuan; Qiu, Weiyuan; Roesch, Pascale; Tan, Lei; Yin, Yongcheng

doi:10.1090/S1088-4173-10-00201-8

A tableau approach of the KSS nest
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by Wenjuan Peng, Weiyuan Qiu, Pascale Roesch, Lei Tan and Yongcheng Yin

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

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

Published electronically: February 18, 2010

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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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