Simple Flows on Tori with Uncommon Chaos

    2020, Volume 25, Number 2, pp.  199-214

    Author(s): Simó C.

    We consider a family of simple flows in tori that display chaotic behavior in a wide sense. But these flows do not have homoclinic nor heteroclinic orbits. They have only a fixed point which is of parabolic type. However, the dynamics returns infinitely many times near the fixed point due to quasi-periodicity. A preliminary example is given for maps introduced in a paper containing many examples of strange attractors in [6]. Recently, a family of maps similar to the flows considered here was studied in [9]. In the present paper we consider the case of 2D tori and the extension to tori of arbitrary finite dimension. Some other facts about exceptional frequencies and behavior around parabolic fixed points are also included.
    Keywords: chaos without homoclinic/heteroclinic points, chaotic flows on tori, the returning role of quasi-periodicity, zero maximal Lyapunov exponents, the role of parabolic points, exceptional frequencies
    Citation: Simó C., Simple Flows on Tori with Uncommon Chaos, Regular and Chaotic Dynamics, 2020, Volume 25, Number 2, pp. 199-214

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