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arXiv · 2202.01282

Upper bounds for the moduli of polynomial-like maps

Alexander Blokh·Lex Oversteegen·Vladlen Timorin
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Abstract

We establish a version of the Pommerenke-Levin-Yoccoz inequality for the modulus of a polynomial-like restriction of a global polynomial and give two applications. First it is shown that if the modulus of a polynomial-like restriction of an arbitrary polynomial is bounded from below then this forces bounded combinatorics. The second application concerns parameter slices of cubic polynomials given by a non-repelling value of a fixed point multiplier. Namely, the intersection of the main cubioid and the multiplier slice lies in the closure of the principal hyperbolic domain, with only possible exception of queer components.

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Alexander Blokh, Lex Oversteegen, Vladlen Timorin. 2022-02-02. Upper bounds for the moduli of polynomial-like maps. https://arxiv.org/abs/2202.01282

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