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Holomorphic motions for unicritical correspondences.
- Source :
- Nonlinearity; Aug2017, Vol. 30 Issue 8, p1-1, 1p
- Publication Year :
- 2017
-
Abstract
- We study quasiconformal deformations and mixing properties of hyperbolic sets in the family of holomorphic correspondences z<superscript>r</superscript> + 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]
- Subjects :
- DYNAMICS
PARAMETRIC equations
CURVILINEAR motion
GEOMETRY
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 09517715
- Volume :
- 30
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- Nonlinearity
- Publication Type :
- Academic Journal
- Accession number :
- 124260572
- Full Text :
- https://doi.org/10.1088/1361-6544/aa7736