Lattès-type mappings on compact manifolds

Author:

Astola Laura,Kangaslampi Riikka,Peltonen Kirsi

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 C ¯ \bar {\mathbb {C}} . 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.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology

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