## Preprint ims14-03

Tanya Firsova, Mikhail Lyubich
$\lambda$-Lemma for families of Riemann surfaces and the critical loci of complex H\'enon map

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

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