Uniformly quasiregular mappings of Lattès type

Lundi 14 novembre 2011 14:00-15:00 - Riikka Kangaslampi - Université Paris-Sud et Aalto University

Résumé : 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 complex 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 mappings with different Julia sets. We give examples of mappings having lower dimensional sphere, projective space, and 2-torus as Julia sets.
This talk is based on the following two papers :
L. Astola, R. Kangaslampi, and K. Peltonen, Lattès-type mappings on compact manifolds, Conformal Geometry and Dynamics 14, 2010, pp. 337-367.
R. Kangaslampi, K. Peltonen, and J.-M. Wu, Uniformly quasiregular maps with toroidal Julia sets, Preprint, 2011.

Lieu : bât. 425 - 113-115

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