Holomorphic motions for unicritical correspondences
Abstract
We study quasiconformal deformations and mixing properties of hyperbolic sets in the family of holomorphic correspondences zr +c, where r >1 is rational. Julia sets in this family are projections of Julia sets of holomorphic maps on C2, which are skew-products when r is integer, and solenoids when r is non-integer and c is close to zero. Every hyperbolic Julia set in C2 moves holomorphically. The projection determines a branched holomorphic motion with local (and sometimes global) parameterisations of the plane Julia set by quasiconformal curves.
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