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Conformal Geometry and Dynamics

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$ \lambda$-lemma for families of Riemann surfaces and the critical loci of complex Hénon maps


Authors: Tanya Firsova and Mikhail Lyubich
Journal: Conform. Geom. Dyn. 21 (2017), 111-125
MSC (2010): Primary 32G15, 32H50, 37F10, 37F30
DOI: https://doi.org/10.1090/ecgd/300
Published electronically: March 16, 2017
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Abstract: We prove a version of the classical $ \lambda $-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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Additional Information

Tanya Firsova
Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
Email: tanyaf@math.ksu.edu

Mikhail Lyubich
Affiliation: Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York 11794
Email: mlyubich@math.stonybrook.edu

DOI: https://doi.org/10.1090/ecgd/300
Received by editor(s): August 13, 2014
Received by editor(s) in revised form: April 9, 2016
Published electronically: March 16, 2017
Additional Notes: The research of the second author was supported in part by NSF
Article copyright: © Copyright 2017 American Mathematical Society