Zobrazeno 1 - 10
of 155
pro vyhledávání: '"37F10, 30D05"'
Autor:
Bergweiler, Walter, Ding, Jie
Let $f$ be a transcendental entire function of finite order which has an attracting periodic point $z_0$ of period at least $2$. Suppose that the set of singularities of the inverse of $f$ is finite and contained in the component $U$ of the Fatou set
Externí odkaz:
http://arxiv.org/abs/2407.19963
Autor:
Das, Sukanta, Nayak, Tarakanta
This article studies the singular values of entire functions of the form $E^k (z)+P(z)$ where $E^k$ denotes the $k-$times composition of $e^z$ with itself and $P$ is any non-constant polynomial. It is proved that the full preimage of each neighborhoo
Externí odkaz:
http://arxiv.org/abs/2407.14835
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
Autor:
Rempe, Lasse
"Phase-locking" is a fundamental phenomenon in which coupled or periodically forced oscillators synchronise. The Arnold family of circle maps, which describes a forced oscillator, is the simplest mathematical model of phase-locking and has been studi
Externí odkaz:
http://arxiv.org/abs/2309.06595
Autor:
Cui, Weiwei, Wang, Jun
We construct exponential maps for which the singular value tends to infinity under iterates while the maps are ergodic. This is in contrast with a result of Lyubich from 1987 which tells that $e^z$ is not ergodic.
Comment: 11 pages, 1 figure; co
Comment: 11 pages, 1 figure; co
Externí odkaz:
http://arxiv.org/abs/2308.10565
Let $f$ be a degree $d$ bicritical rational map with critical point set $\mathcal{C}_f$ and critical value set $\mathcal{V}_f$. Using the group $\textrm{Deck}(f^k)$ of deck transformations of $f^k$, we show that if $g$ is a bicritical rational map wh
Externí odkaz:
http://arxiv.org/abs/2209.08012
Autor:
Bergweiler, Walter, Cui, Weiwei
Publikováno v:
Int. Math. Res. Not. IMRN 2024, no. 9, 7281-7306
Bergweiler and Kotus gave sharp upper bounds for the Hausdorff dimension of the escaping set of a meromorphic function in the Eremenko-Lyubich class, in terms of the order of the function and the maximal multiplicity of the poles. We show that these
Externí odkaz:
http://arxiv.org/abs/2209.06270
Autor:
Aspenberg, Magnus, Cui, Weiwei
Publikováno v:
Comm. Math. Phys. 405 (2024), no. 2, Paper No. 55
We propose a notion of Misiurewicz condition for transcendental entire functions and study perturbations of Speiser functions satisfying this condition in their parameter spaces (in the sense of Eremenko and Lyubich). We show that every Misiurewicz e
Externí odkaz:
http://arxiv.org/abs/2209.00385
Autor:
Aspenberg, Magnus, Cui, Weiwei
Publikováno v:
J. Anal. Math. 153 (2024), no. 2, 759-775
We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which comple
Externí odkaz:
http://arxiv.org/abs/2206.11093
Autor:
Wolff, Mareike
We show that there exists a transcendental entire function whose Julia set has positive finite Lebesgue measure.
Comment: 6 pages, 2 figures
Comment: 6 pages, 2 figures
Externí odkaz:
http://arxiv.org/abs/2204.11089