On the classification of laminations associated to quadratic polynomials

Details On the classification of laminations associated to quadratic polynomials On the classification of laminations associated to quadratic polynomials

2007-03-06

arxiv.org/abs/math/0703159v1

Mathematics

Dynamical Systems

Scientific paper

Given any rational map $f$, there is a lamination by Riemann surfaces associated to $f$. Such laminations were constructed in general by Lyubich and Minsky. In this paper, we classify laminations associated to quadratic polynomials with periodic critical point. In particular, we prove that the topology of such laminations determines the combinatorics of the parameter. We also describe the topology of laminations associated to other types of quadratic polynomials.

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