Dynamical systems with Lipschitz inverse shadowing properties › Научные исследования в СПбГУ

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Dynamical systems with Lipschitz inverse shadowing properties. / Pilyugin, S. Yu; Vol'fson, G. I.; Todorov, D. I.

в: Vestnik St. Petersburg University: Mathematics, Том 44, № 3, 09.2011, стр. 208-213.

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

Harvard

Pilyugin, SY, Vol'fson, GI & Todorov, DI 2011, 'Dynamical systems with Lipschitz inverse shadowing properties', Vestnik St. Petersburg University: Mathematics, Том. 44, № 3, стр. 208-213. https://doi.org/10.3103/S106345411103006X

APA

Pilyugin, S. Y., Vol'fson, G. I., & Todorov, D. I. (2011). Dynamical systems with Lipschitz inverse shadowing properties. Vestnik St. Petersburg University: Mathematics, 44(3), 208-213. https://doi.org/10.3103/S106345411103006X

Vancouver

Pilyugin SY, Vol'fson GI, Todorov DI. Dynamical systems with Lipschitz inverse shadowing properties. Vestnik St. Petersburg University: Mathematics. 2011 Сент.;44(3):208-213. https://doi.org/10.3103/S106345411103006X

Author

Pilyugin, S. Yu ; Vol'fson, G. I. ; Todorov, D. I. / Dynamical systems with Lipschitz inverse shadowing properties. в: Vestnik St. Petersburg University: Mathematics. 2011 ; Том 44, № 3. стр. 208-213.

BibTeX

@article{371dd4ace0b84108b94ba3ff5bf8c5b5,

title = "Dynamical systems with Lipschitz inverse shadowing properties",

abstract = "In this paper, the notion of the Lipschitz inverse shadowing property with respect to two classes of d-methods that generate pseudotrajectories of dynamical systems is introduced. It is shown that if a diffeomorphism of a Euclidean space has the Lipschitz inverse shadowing property on the trajectory of an individual point, then the Ma{\~n}{\'e} analytic strong transversality condition must be satisfied at this point. This result is used in the proof of the main theorem: a diffeomorphism of a smooth closed manifold that has the Lipschitz inverse shadowing property is structurally stable.",

keywords = "dynamical systems, inverse shadowing, structural stability, transversality",

author = "Pilyugin, {S. Yu} and Vol'fson, {G. I.} and Todorov, {D. I.}",

year = "2011",

month = sep,

doi = "10.3103/S106345411103006X",

language = "English",

volume = "44",

pages = "208--213",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Dynamical systems with Lipschitz inverse shadowing properties

AU - Pilyugin, S. Yu

AU - Vol'fson, G. I.

AU - Todorov, D. I.

PY - 2011/9

Y1 - 2011/9

N2 - In this paper, the notion of the Lipschitz inverse shadowing property with respect to two classes of d-methods that generate pseudotrajectories of dynamical systems is introduced. It is shown that if a diffeomorphism of a Euclidean space has the Lipschitz inverse shadowing property on the trajectory of an individual point, then the Mañé analytic strong transversality condition must be satisfied at this point. This result is used in the proof of the main theorem: a diffeomorphism of a smooth closed manifold that has the Lipschitz inverse shadowing property is structurally stable.

AB - In this paper, the notion of the Lipschitz inverse shadowing property with respect to two classes of d-methods that generate pseudotrajectories of dynamical systems is introduced. It is shown that if a diffeomorphism of a Euclidean space has the Lipschitz inverse shadowing property on the trajectory of an individual point, then the Mañé analytic strong transversality condition must be satisfied at this point. This result is used in the proof of the main theorem: a diffeomorphism of a smooth closed manifold that has the Lipschitz inverse shadowing property is structurally stable.

KW - dynamical systems

KW - inverse shadowing

KW - structural stability

KW - transversality

UR - http://www.scopus.com/inward/record.url?scp=84859702061&partnerID=8YFLogxK

U2 - 10.3103/S106345411103006X

DO - 10.3103/S106345411103006X

M3 - Article

AN - SCOPUS:84859702061

VL - 44

SP - 208

EP - 213

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 74986010