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On the classification of laminations associated to quadratic polynomials

2007/03/06 by Carlos Cabrera, Cabrera, Carlos
Mathematics · #37B45 #37F10 #37F20 #37F45 #37F50 #46M40 #Advanced Differential Equations and Dynamical Systems #Analytic Number Theory Research #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/0703159

openalex publication_date 2007/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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