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

    Received 24 March 2015

    2016, Vol. 12, No. 1, pp.  3-15

    Author(s): Matyushkin I. V.

    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

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