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Nelin. Dinam., 2016, Volume 12, Number 1, Pages 3–15 (Mi nd509)  

This article is cited in 1 scientific paper (total in 1 paper)

Original papers

On some properties of an $\exp(iz)$ map

I. V. Matyushkin

Molecular Electronics Research Institute, Zapadnyj 1st valley, 12, building 1, Zelenograd, Moscow, 124460, Russia

Abstract: The properties of an $e^{iz}$ map are studied. It is proved that the map has one stable and an infinite number of unstable equilibrium positions. There are an infinite number of repellent twoperiodic cycles. The nonexistence of wandering points is heuristically shown by using MATLAB. The definition of helicity points is given. As for other hyperbolic maps, Cantor bouquets are visualized for the Julia and Mandelbrot sets.

Keywords: holomorphic dynamics, fractal, Cantor bouquet, hyperbolic map

Full text: PDF file (8656 kB)
References: PDF file   HTML file
UDC: 517.542
MSC: 30C20
Received: 24.03.2015
Revised: 16.01.2016

Citation: I. V. Matyushkin, “On some properties of an $\exp(iz)$ map”, Nelin. Dinam., 12:1 (2016), 3–15

Citation in format AMSBIB
\Bibitem{Mat16}
\by I.~V.~Matyushkin
\paper On some properties of an $\exp(iz)$ map
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 1
\pages 3--15
\mathnet{http://mi.mathnet.ru/nd509}


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    This publication is cited in the following articles:
    1. I. V. Matyushkin, M. A. Zapletina, “Experimental research of iterated dynamics for the complex exponentials with linear term”, European Conference - Workshop Nonlinear Maps and Applications, Journal of Physics Conference Series, 990, IOP Publishing Ltd, 2018, UNSP 012008  crossref  mathscinet  isi  scopus
  • Нелинейная динамика
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