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Holomorphic correspondences mating Chebyshev-like maps with Hecke groups
Published online by Cambridge University Press: 04 July 2005
Abstract
We prove structure theorems for holomorphic correspondences realizing matings between pinched polynomial-like maps with connected Julia sets and Hecke groups (Fuchsian representations of free products C2 * Cn of cyclic groups of orders 2 and n). We show that such matings are generated by two-to-two subcorrespondences if and only if the maps are Chebyshev-like. We describe the dynamical behaviour of these matings in detail in the case n = 4 and we present a conjectured combinatorial description of the connectedness locus in parameter space in this case.
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- 2005 Cambridge University Press
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