Abstract
The iterates of a uniformly quasiregular map acting on a Riemannian manifold are quasiregular with a uniform bound on the dilatation. There is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We construct the first examples of uniformly quasiregular mappings that have a 2-torus as the Julia set. The spaces supporting this type of mappings include the Hopf link complement and its lens space quotients.
Original language | English (US) |
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Pages (from-to) | 81-88 |
Number of pages | 8 |
Journal | Conformal Geometry and Dynamics |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - Mar 21 2012 |
Externally published | Yes |
Keywords
- Conformal structure
- Julia set
- Lattès-type mapping
- Lens space
- Uniformly quasiregular mapping
ASJC Scopus subject areas
- Geometry and Topology