Zobrazeno 1 - 10
of 27 678
pro vyhledávání: '"A A, Eremenko"'
Autor:
Rempe, Lasse
Consider the entire function $f(z)=\cosh(z)$. We show that the escaping set of this function - that is, the set of points whose orbits tend to infinity under iteration - has a structure known as a "spider's web". This disproves a conjecture of Sixsmi
Externí odkaz:
http://arxiv.org/abs/2410.20998
Autor:
Brown, Andrew P.
Let $f\colon\mathbb{C} \to\mathbb{C}$ be a transcendental entire function. In 1989, Eremenko asked the following question concerning the set $I(f)$ of points that tend to infinity under iteration: can every point of $I(f)$ be joined to $\infty$ by a
Externí odkaz:
http://arxiv.org/abs/2405.08811
Autor:
Kumar, Dinesh, Das, Soumyajeet
In this paper, we have discussed the dynamics of composite entire functions in terms of relationship between bungee set, repelling periodic points (to be denoted by $RP$) and rationally indifferent fixed point set. We have established relation betwee
Externí odkaz:
http://arxiv.org/abs/2405.11217
Akademický článek
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Autor:
Rempe, Lasse
Eremenko and Lyubich proved that an entire function whose set of singular values is bounded is expanding at points where its image has large modulus. These expansion properties have been at the centre of the subsequent study of this class of function
Externí odkaz:
http://arxiv.org/abs/2105.09053
Autor:
Langley, J. K.
The Bank-Laine conjecture concerning the oscillation of solutions of second order homogeneous linear differential equations has recently been disproved by Bergweiler and Eremenko. It is shown here, however, that the conjecture is true if the set of f
Externí odkaz:
http://arxiv.org/abs/1804.04388
Publikováno v:
Proc. Lond. Math. Soc. (3) 120 (2020), no. 2, 155-191
Recently Bishop constructed the first example of a bounded-type transcendental entire function with a wandering domain using a new technique called quasiconfomal folding. It is easy to check that his method produces an entire function of infinite ord
Externí odkaz:
http://arxiv.org/abs/1807.11820
Autor:
Bergweiler, Walter
Publikováno v:
Proceedings of the American Mathematical Society, 2002 Nov 01. 130(11), 3231-3236.
Externí odkaz:
https://www.jstor.org/stable/1194148
Akademický článek
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Autor:
Rippon, P. J., Stallard, G. M.
Publikováno v:
Proceedings of the American Mathematical Society, 2005 Apr 01. 133(4), 1119-1126.
Externí odkaz:
https://www.jstor.org/stable/4097671