Uniformly quasiregular maps with toroidal julia sets

Riikka Kangaslampi, Kirsi Peltonen, Jang Mei Wu

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)81-88
Number of pages8
JournalConformal Geometry and Dynamics
Volume16
Issue number4
DOIs
StatePublished - Mar 21 2012

Keywords

  • Conformal structure
  • Julia set
  • Lattès-type mapping
  • Lens space
  • Uniformly quasiregular mapping

ASJC Scopus subject areas

  • Geometry and Topology

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