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Matematicheskie Zametki, 2023, Volume 113, Issue 2, Pages 182–196
DOI: https://doi.org/10.4213/mzm13527 (Mi mzm13527) 		 
On a Problem of V. V. Nemytskii

B. S. Kalitin

Belarusian State University, Minsk
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DOI: https://doi.org/10.4213/mzm13527
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.
Keywords: dynamical system, invariant set, attraction, elliptic point.
Received: 04.04.2022
Revised: 12.07.2022
English version:
Mathematical Notes, 2023, Volume 113, Issue 2, Pages 200–211
DOI: https://doi.org/10.1134/S0001434623010236
Bibliographic databases:
Document Type: Article
UDC: 517.938:925
Language: Russian
Citation: B. S. Kalitin, “On a Problem of V. V. Nemytskii”, Mat. Zametki, 113:2 (2023), 182–196; Math. Notes, 113:2 (2023), 200–211
Citation in format AMSBIB
\Bibitem{Kal23}
\by B.~S.~Kalitin
\paper On a Problem of V.~V.~Nemytskii
\jour Mat. Zametki
\yr 2023
\vol 113
\issue 2
\pages 182--196
\mathnet{http://mi.mathnet.ru/mzm13527}
\crossref{https://doi.org/10.4213/mzm13527}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4563361}
\transl
\jour Math. Notes
\yr 2023
\vol 113
\issue 2
\pages 200--211
\crossref{https://doi.org/10.1134/S0001434623010236}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149960545}
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