λ-Lemma for families of Riemann surfaces and the critical loci of complex Hénon maps

2014/04/15 by Tanya Firsova, Firsova, Tanya, Mikhail Lyubich +1
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1404.3910

openalex publication_date 2014/04/15 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We prove a version of the classical λ-lemma for holomorphic families of Riemann surfaces. We then use it to show that critical loci for complex Hénon maps that are small perturbations of quadratic polynomials with Cantor Julia sets are all quasiconformally equivalent.

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