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# Igor Matyushkin

 Matyushkin I. V. On some properties of an ${\rm exp}(iz)$ map 2016, Vol. 12, No. 1, pp.  3-15 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 Citation: Matyushkin I. V.,  On some properties of an ${\rm exp}(iz)$ map , Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 1, pp.  3-15 DOI:10.20537/nd1601001