Lattès-type mappings on compact manifolds

L.J. Astola, R. Kangaslampi, K. Peltonen

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Abstract

A uniformly quasiregular mapping acting on a compact Riemannian manifold distorts the metric by a bounded amount, independently of the number of iterates. Such maps are rational with respect to some measurable conformal structure and there is a Fatou-Julia type theory associated with the dynamical system obtained by iterating these mappings. We study a rich subclass of uniformly quasiregular mappings that can be produced using an analogy of classical Lattès' construction of chaotic rational functions acting on the extended plane . We show that there is a plenitude of compact manifolds that support these mappings. Moreover, we find that in some cases there are alternative ways to construct this type of mapping with different Julia sets.
Original languageEnglish
Pages (from-to)337-367
Number of pages31
JournalConformal Geometry and Dynamics
Volume14
Publication statusPublished - 2010

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Astola, L. J., Kangaslampi, R., & Peltonen, K. (2010). Lattès-type mappings on compact manifolds. Conformal Geometry and Dynamics, 14, 337-367.