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On a Problem of V. V. Nemytskii

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Abstract

We study trajectories in a neighborhood of attractors and weak attractors of dynamical systems on a metric space. The properties of elliptic and weakly elliptic points of compact invariant sets are studied. A solution of the generalized problem of V. V. Nemytskii concerning the existence of compact invariant sets of weakly elliptic type for the case of asymptotically compact dynamical systems is given.

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Authors and Affiliations

  1. Belarusian State University, Minsk, 220030, Belarus

    B. S. Kalitine

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  1. B. S. Kalitine
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Correspondence to B. S. Kalitine.

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Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 182–196 https://doi.org/10.4213/mzm13527.

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Kalitine, B.S. On a Problem of V. V. Nemytskii. Math Notes 113, 200–211 (2023). https://doi.org/10.1134/S0001434623010236

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