2022/02/02 by Blokh, Alexander, Oversteegen, Lex, Timorin, Vladlen
#37F10 (Secondary) #37F20 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2202.01282
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.