Holomorphic motions for unicritical correspondences
Dynamical Systems
2017-08-02 v2
Abstract
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 C^2, 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 C^2 moves holomorphically. The projection determines a branched holomorphic motion with local (and sometimes global) parameterisations of the plane Julia set by quasiconformal curves.
Cite
@article{arxiv.1608.04333,
title = {Holomorphic motions for unicritical correspondences},
author = {Carlos Siqueira and Daniel Smania},
journal= {arXiv preprint arXiv:1608.04333},
year = {2017}
}
Comments
23 pages, 1 figure (final corrected version accepted for publication)