Uniformly quasiregular maps with toroidal julia sets

Riikka Kangaslampi; Kirsi Peltonen; Jang Mei Wu

doi:10.1090/S1088-4173-2012-00235-4

Uniformly quasiregular maps with toroidal julia sets

Riikka Kangaslampi, Kirsi Peltonen, Jang Mei Wu

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	81-88
Number of pages	8
Journal	Conformal Geometry and Dynamics
Volume	16
Issue number	4
DOIs	https://doi.org/10.1090/S1088-4173-2012-00235-4
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

Online availability

10.1090/S1088-4173-2012-00235-4

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AU - Peltonen, Kirsi

AU - Wu, Jang Mei

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Y1 - 2012/3/21

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AB - 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.

KW - Conformal structure

KW - Julia set

KW - Lattès-type mapping

KW - Lens space

KW - Uniformly quasiregular mapping

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JO - Conformal Geometry and Dynamics

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Uniformly quasiregular maps with toroidal julia sets

Abstract

Keywords

ASJC Scopus subject areas

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