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Tessellation and Lyubich–Minsky laminations associated with quadratic maps, I: pinching semiconjugacies

Published online by Cambridge University Press:  01 April 2009

TOMOKI KAWAHIRA
TOMOKI KAWAHIRA*
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japan (email: [email protected])
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Abstract

We construct tessellations of the filled Julia sets of hyperbolic and parabolic quadratic maps. The dynamics inside the Julia sets are then organized by tiles which play the role of the external rays outside. We also construct continuous families of pinching semiconjugacies associated with hyperbolic-to-parabolic degenerations without using quasiconformal deformation. Instead, we achieve this via tessellation and investigation of the hyperbolic-to-parabolic degeneration of linearizing coordinates inside the Julia set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 2 , April 2009 , pp. 579 - 612
Copyright
Copyright © Cambridge University Press 2008

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