Slow escaping points of quasiregular mappings
نویسندگان
چکیده
منابع مشابه
Slow Escaping Points of Meromorphic Functions
We show that for any transcendental meromorphic function f there is a point z in the Julia set of f such that the iterates fn(z) escape, that is, tend to ∞, arbitrarily slowly. The proof uses new covering results for analytic functions. We also introduce several slow escaping sets, in each of which fn(z) tends to ∞ at a bounded rate, and establish the connections between these sets and the Juli...
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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...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2016
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-016-1687-9