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Linear Recurrent Equations in the Space of Convex Compact Sets and the Diameters of Their Solutions

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Abstract

In the space of convex compact sets with the Minkowski addition operation and the operation of multiplication of a matrix by a set, we consider linear recurrent equations of the first order. We give a complete description of such equations whose all solutions have a constant diameter. For equations of a special form, the Lyapunov exponents of the sequences of diameters of their solutions are calculated.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Belarus, Minsk, 220072, Belarus

    A. S. Voidelevich

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  1. A. S. Voidelevich
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Correspondence to A. S. Voidelevich.

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Translated by V. Potapchouck

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Voidelevich, A.S. Linear Recurrent Equations in the Space of Convex Compact Sets and the Diameters of Their Solutions. Diff Equat 59, 1090–1094 (2023). https://doi.org/10.1134/S0012266123080074

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  • DOI: https://doi.org/10.1134/S0012266123080074

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