On a Problem of V. V. Nemytskii

B. S. Kalitin

Belarusian State University, Minsk

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.

UDC: 517.938:925

Received: 04.04.2022
Revised: 12.07.2022

DOI: 10.4213/mzm13527

 English version: Mathematical Notes, 2023, 113:2, 200–211

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