Holomorphic motions for unicritical correspondences.

We study quasiconformal deformations and mixing properties of hyperbolic sets in the family of holomorphic correspondences z^r  +  c, where r  >  1 is rational. Julia sets in this family are projections of Julia sets of holomorphic maps on 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 moves holomorphically. The projection determines a branched holomorphic motion with local (and sometimes global) parameterizations of the plane Julia set by quasiconformal curves. [ABSTRACT FROM AUTHOR]