Dynamics of quadratic polynomials: Complex bounds for real maps

1995/04/01 by Mikhail Lyubich, Lyubich, Mikhail, Michael Yampolsky +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.math/9504206

openalex publication_date 1995/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend Sullivan's complex a priori bounds to real quadratic polynomials with essentially bounded combinatorics. Combined with the previous results of the first author, this yields complex bounds for all real quadratics. Local connectivity of the corresponding Julia sets follows.

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