Tessellation and Lyubich-Minsky laminations associated with quadratic maps I: Pinching semiconjugacies

Details Tessellation and Lyubich-Minsky laminations associated with quadratic maps I: Pinching semiconjugacies Tessellation and Lyubich-Minsky laminations associated with quadratic maps I: Pinching semiconjugacies

2006-09-11

arxiv.org/abs/math/0609280v1

Mathematics

Dynamical Systems

34 pages including 2 of 13 figures. To get the original, visit http://www.math.nagoya-u.ac.jp/~kawahira/works/tessellation.pdf

Scientific paper

We introduce tessellation of the filled Julia sets for hyperbolic and parabolic quadratic maps. Then the dynamics inside their Julia sets are organized by tiles which work like external rays outside. We also construct continuous families of pinching semiconjugacies associated with hyperblic-to-parabolic degenerations without using quasiconformal deformation. Instead we use tessellation and investigation on the hyperbolic-to-parabolic degeneration of linearizing coordinates inside the Julia set.

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