λ-lemma for families of riemann surfaces and the critical loci of complex hénon maps

Tanya Firsova; Mikhail Lyubich

doi:10.1090/ecgd/300

λ-lemma for families of riemann surfaces and the critical loci of complex hénon maps

Tanya Firsova
, Mikhail Lyubich

Mathematical Science Institute

Kansas State University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	111-125
Number of pages	15
Journal	Conformal Geometry and Dynamics
Volume	21
Issue number	6
DOIs	https://doi.org/10.1090/ecgd/300
State	Published - 2017

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title = "λ-lemma for families of riemann surfaces and the critical loci of complex h{\'e}non maps",

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 H{\'e}non maps that are small perturbations of quadratic polynomials with Cantor Julia sets are all quasiconformally equivalent.",

author = "Tanya Firsova and Mikhail Lyubich",

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year = "2017",

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journal = "Conformal Geometry and Dynamics",

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AU - Firsova, Tanya

AU - Lyubich, Mikhail

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AB - 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.

UR - https://www.scopus.com/pages/publications/85015338690

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DO - 10.1090/ecgd/300

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AN - SCOPUS:85015338690

SN - 1088-4173

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SP - 111

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JO - Conformal Geometry and Dynamics

JF - Conformal Geometry and Dynamics

IS - 6

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λ-lemma for families of riemann surfaces and the critical loci of complex hénon maps

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