منابع مشابه
Examples of Uniformly Quasiregular Mappings
In this paper we construct examples of uniformly quasiregular (uqr) mappings. These provide counterexamples for a rigidity conjecture in quasiregular dynamics. It states that a closed manifold of dimension at least three, which admits a branched uqr mapping, is quasiconformally equivalent to an ordinary sphere Sn. 1. Statements and results In this paper we construct examples of a certain type o...
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Let G be a semigroup of K-quasiregular or K-quasimeromorphic functions mapping a given open set U in the Riemann sphere into itself, for a xed K , the semigroup operation being the composition of functions. We prove that if G satisses an algebraic condition, which is true for all abelian semigroups, then there exists a K-quasiconformal homeomorphism of U onto an open set V such that all the fun...
متن کاملUniformly Quasiregular Mappings of Lattès Type
Using an analogy of the Lattès’ construction of chaotic rational functions, we show that there are uniformly quasiregular mappings of the nsphere R whose Julia set is the whole sphere. Moreover there are analogues of power mappings, uniformly quasiregular mappings whose Julia set is Sn−1 and its complement in Sn consists of two superattracting basins. In the chaotic case we study the invariant ...
متن کاملUniformly Quasiregular Maps with Toroidal Julia Sets
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 incl...
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We consider rigidity phenomena for holomorphic functions and then more generally for uniformly quasiregular maps.
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2020
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2020.51