منابع مشابه
On Injectivity of Quasiregular Mappings
We give sufficient conditions for a planar quasiregular mapping to be injective in terms of the range of the differential matrix.
متن کاملSingularities of quasiregular mappings on Carnot groups
In 1970 Poletskĭı applied the method of the module of a family of curves to describe behavior of quasiregular mappings (in another terminology mappings with bounded distortion) in Rn. In the present paper we generalize a result by Poletskĭı and study a singular set of a quasiregular mapping using the method of the module of a families of curves on Carnot groups.
متن کاملExamples 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...
متن کاملQuasiregular Mappings of Polynomial Type in R
Complex dynamics deals with the iteration of holomorphic functions. As is well known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of Julia sets and the Mandelbrot set. In the same spirit, this article aims to study the dynamics of the simplest non-trivial quasiregular mappings. These are mappi...
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 ...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Series A I Mathematica
سال: 1975
ISSN: 0066-1953
DOI: 10.5186/aasfm.1975.0109