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Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, Volume 7, Issue 2, Pages 289–296
DOI: https://doi.org/10.21638/11701/spbu01.2020.211 (Mi vspua190) 		 
This article is cited in 1 scientific paper (total in 1 paper)

IN MEMORIAM OF V. A. PLISS

On problems of the theory of stability of weakly hyperbolic invariant sets

N. A. Begunab

a St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
b Tarbiat Modares University, P. O. Box: 14115-111, Tehran, Iran
Full-text PDF (434 kB) Citations (1)
DOI: https://doi.org/10.21638/11701/spbu01.2020.211
Abstract: This paper represents a brief survey of the theory of stability of weakly hyperbolic invariant sets. In a series of papers published by the author together with V. A. Pliss and G. R. Sell, it was proved that a weakly hyperbolic invariant set is stable even in the absence of the Lipschitz condition. However, the question of uniqueness of leafs of a weakly hyperbolic invariant set of a perturbed system remains open. The paper shows the relationship of this problem with the so-called plaque expansivity conjecture in the theory of dynamical systems.
Keywords: stability, weak hyperbolicity, leaf set, perturbed system, singularity, plaque espansivity conjecture.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00388
18-01-00230
The work is supported by Russian Foundation for Basic Research (grants 19-01-00388, 18-01-00230).
Received: 24.10.2019
Revised: 10.12.2019
Accepted: 12.12.2019
English version:
Vestnik St. Petersburg University, Mathematics, 2020, Volume 7, Issue 2, Pages 191–196
DOI: https://doi.org/10.1134/S1063454120020065
Document Type: Article
UDC: 517.938
MSC: 37D10, 37D40
Language: Russian
Citation: N. A. Begun, “On problems of the theory of stability of weakly hyperbolic invariant sets”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 7:2 (2020), 289–296; Vestn. St. Petersbg. Univ., Math., 7:2 (2020), 191–196
Citation in format AMSBIB
\Bibitem{Beg20}
\by N.~A.~Begun
\paper On problems of the theory of stability of weakly hyperbolic invariant sets
\jour Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy
\yr 2020
\vol 7
\issue 2
\pages 289--296
\mathnet{http://mi.mathnet.ru/vspua190}
\crossref{https://doi.org/10.21638/11701/spbu01.2020.211}
\transl
\jour Vestn. St. Petersbg. Univ., Math.
\yr 2020
\vol 7
\issue 2
\pages 191--196
\crossref{https://doi.org/10.1134/S1063454120020065}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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