Standard

On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets. / Begun, N. A.

в: Vestnik St. Petersburg University: Mathematics, Том 53, № 2, 01.04.2020, стр. 191-196.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Begun, NA 2020, 'On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets', Vestnik St. Petersburg University: Mathematics, Том. 53, № 2, стр. 191-196. https://doi.org/10.1134/S1063454120020065

APA

Begun, N. A. (2020). On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets. Vestnik St. Petersburg University: Mathematics, 53(2), 191-196. https://doi.org/10.1134/S1063454120020065

Vancouver

Begun NA. On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets. Vestnik St. Petersburg University: Mathematics. 2020 Апр. 1;53(2):191-196. https://doi.org/10.1134/S1063454120020065

Author

Begun, N. A. / On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets. в: Vestnik St. Petersburg University: Mathematics. 2020 ; Том 53, № 2. стр. 191-196.

BibTeX

@article{38af601c39e449899e041e2aa04bc04d,
title = "On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets",
abstract = "This paper presents a brief survey for the theory of stability of weakly hyperbolic invariant sets. It has been proved in several papers that I published along with Pliss and Sell that a weakly hyperbolic invariant set is stable even if the Lipschitz condition fails to hold. However, the uniqueness of leaves of a weakly hyperbolic invariant set of a perturbed system remains an open question. We show that this problem is connected to the so-called plaque expansivity conjecture in the theory of dynamical systems.",
keywords = "слабая гиперболичность, листовое множество, единственность, возмущенная система, гипотеза экспансивности по площадкам, leaf set, perturbed system, plaque expansivity, stability, uniqueness, weak hyperbolicity, ATTRACTORS, SYSTEMS, MANIFOLDS",
author = "Begun, {N. A.}",
note = "Funding Information: This work was supported by the Russian Foundation for Basic Research, grants nos. 19-01-00388 and 18-01-00230. Publisher Copyright: {\textcopyright} 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = apr,
day = "1",
doi = "10.1134/S1063454120020065",
language = "English",
volume = "53",
pages = "191--196",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - On Problems of Stability Theory for Weakly Hyperbolic Invariant Sets

AU - Begun, N. A.

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research, grants nos. 19-01-00388 and 18-01-00230. Publisher Copyright: © 2020, Pleiades Publishing, Ltd. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/4/1

Y1 - 2020/4/1

N2 - This paper presents a brief survey for the theory of stability of weakly hyperbolic invariant sets. It has been proved in several papers that I published along with Pliss and Sell that a weakly hyperbolic invariant set is stable even if the Lipschitz condition fails to hold. However, the uniqueness of leaves of a weakly hyperbolic invariant set of a perturbed system remains an open question. We show that this problem is connected to the so-called plaque expansivity conjecture in the theory of dynamical systems.

AB - This paper presents a brief survey for the theory of stability of weakly hyperbolic invariant sets. It has been proved in several papers that I published along with Pliss and Sell that a weakly hyperbolic invariant set is stable even if the Lipschitz condition fails to hold. However, the uniqueness of leaves of a weakly hyperbolic invariant set of a perturbed system remains an open question. We show that this problem is connected to the so-called plaque expansivity conjecture in the theory of dynamical systems.

KW - слабая гиперболичность

KW - листовое множество

KW - единственность

KW - возмущенная система

KW - гипотеза экспансивности по площадкам

KW - leaf set

KW - perturbed system

KW - plaque expansivity

KW - stability

KW - uniqueness

KW - weak hyperbolicity

KW - ATTRACTORS

KW - SYSTEMS

KW - MANIFOLDS

UR - http://www.scopus.com/inward/record.url?scp=85085868274&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2b634334-5169-3428-9bd6-acc08affa17d/

U2 - 10.1134/S1063454120020065

DO - 10.1134/S1063454120020065

M3 - Article

AN - SCOPUS:85085868274

VL - 53

SP - 191

EP - 196

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 71226351