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Stability of Fixed Points for a Class of Quasilinear Cascades in the Space conv ℝn

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Ukrainian Mathematical Journal Aims and scope

We study discrete dynamical systems (cascades) in a semilinear metric space of nonempty convex compacts of the finite-dimensional space. By using the Minkowski and Aleksandrov methods of convex geometry, we establish sufficient conditions for the stability of fixed points. Under certain restrictions imposed on the mappings generating cascades, the problem of asymptotic stability of the fixed points of cascades is reduced to the localization of the roots of a polynomial inside the unit circle in the complex plane. Examples of cascades in the plane are presented.

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Authors and Affiliations

  1. B. Khmel’nitskii Cherkassy National University, Cherkassy, Ukraine

    I. V. Atamas’

  2. Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine

    V. I. Slyn’ko

Authors
  1. I. V. Atamas’
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  2. V. I. Slyn’ko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 9, pp. 1166–1179, September, 2017.

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Atamas’, I.V., Slyn’ko, V.I. Stability of Fixed Points for a Class of Quasilinear Cascades in the Space conv ℝn. Ukr Math J 69, 1354–1369 (2018). https://doi.org/10.1007/s11253-018-1436-9

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  • DOI: https://doi.org/10.1007/s11253-018-1436-9

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