Geodesic
On some properties of an $\exp(iz)$ map
Russian journal of nonlinear dynamics, Tome 12 (2016) no. 1, pp. 3-15

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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, hyperbolic map.
Mots-clés : fractal, Cantor bouquet 
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     author = {I. V. Matyushkin},
     title = {On some properties of an $\exp(iz)$ map},
     journal = {Russian journal of nonlinear dynamics},
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     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2016_12_1_a0/}
}
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I. V. Matyushkin. On some properties of an $\exp(iz)$ map. Russian journal of nonlinear dynamics, Tome 12 (2016) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/ND_2016_12_1_a0/