Uniformly quasiregular maps with toroidal Julia sets
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- by Riikka Kangaslampi, Kirsi Peltonen and Jang-Mei Wu
- Conform. Geom. Dyn. 16 (2012), 81-88
- DOI: https://doi.org/10.1090/S1088-4173-2012-00235-4
- Published electronically: March 21, 2012
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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.References
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Bibliographic Information
- Riikka Kangaslampi
- Affiliation: Aalto University, P.O. Box 11100, 00076 Aalto, Finland
- Email: riikka.kangaslampi@aalto.fi
- Kirsi Peltonen
- Affiliation: Aalto University, P.O. Box 11100, 00076 Aalto, Finland
- Email: kirsi.peltonen@aalto.fi
- Jang-Mei Wu
- Affiliation: Department of Mathematics, University of Illinois, 1409 W. Green Street, Urbana, Illinois 61801-2975
- MR Author ID: 184770
- Email: wu@math.uiuc.edu
- Received by editor(s): October 10, 2011
- Published electronically: March 21, 2012
- Additional Notes: The first author was supported by the Emil Aaltonen Foundation
The second author was supported by the Väisälä Foundation of the Finnish Academy of Science and Letters
The third author was supported by the National Science Foundation Grant DMS-1001669 - © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 16 (2012), 81-88
- MSC (2010): Primary 53A30, 53C20; Secondary 30C65
- DOI: https://doi.org/10.1090/S1088-4173-2012-00235-4
- MathSciNet review: 2899679