Lattès-type mappings on compact manifolds

Lattès-type Mappings on Compact Manifolds

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 ma...

Quasiregular Mappings from a Punctured Ball into Compact Manifolds

We study quasiregular mappings from a punctured unit ball of the Euclidean n-space into compact manifolds. We show that a quasiregular mapping has a limit in the point of punctuation whenever the dimension of the cohomology ring of the compact manifold exceeds a bound given in terms of the dimension and the distortion constant of the mapping.

Surgery on Compact Manifolds

Uv -mappings on Homology Manifolds

A deformation theorem of Bestvina and Walsh [2] states that, below middle and adjacent dimensions, a (k + 1)-connected mapping of a compact topological manifold to compact polyhedron can be deformed to a UV -mapping; that is, a surjection whose fibers are in some sense k-connected. For example, if one has a map f from the n-sphere to the msphere, where n ≤ m, one might expect a typical point in...

Lattès Maps On

In [J. Milnor, On Lattès maps, Dynamics on the Riemann sphere, European Mathematical Society, Zürich, 2006, 9-43], Milnor gave a classification of Lattès maps on P. In this paper, we give a classification of Lattès maps on P. Résumé Dans [J. Milnor, On Lattès maps, Dynamics on the Riemann sphere, European Mathematical Society, Zürich, 2006, 9-43], Milnor a donné une classification des applicati...