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Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold. / Kruk, A. V.; Malykh, A. E.; Reitmann, V.

In: Differential Equations, Vol. 53, No. 13, 01.12.2017, p. 1715-1733.

Research output: Contribution to journal › Article › peer-review

Harvard

Kruk, AV, Malykh, AE & Reitmann, V 2017, 'Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold', Differential Equations, vol. 53, no. 13, pp. 1715-1733. https://doi.org/10.1134/S0012266117130031

APA

Kruk, A. V., Malykh, A. E., & Reitmann, V. (2017). Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold. Differential Equations, 53(13), 1715-1733. https://doi.org/10.1134/S0012266117130031

Vancouver

Kruk AV, Malykh AE, Reitmann V. Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold. Differential Equations. 2017 Dec 1;53(13):1715-1733. https://doi.org/10.1134/S0012266117130031

Author

Kruk, A. V. ; Malykh, A. E. ; Reitmann, V. / Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold. In: Differential Equations. 2017 ; Vol. 53, No. 13. pp. 1715-1733.

BibTeX

@article{b24b866c18fd40549ba16a26a29066f8,
title = "Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold",
abstract = "We prove a generalization of the well-known Douady–Oesterl{\'e} theorem on the upper bound for the Hausdorff dimension of an invariant set of a finite-dimensional mapping to the case of a smooth mapping generating a dynamical system on an infinite-dimensional Hilbert manifold. A similar estimate is given for the invariant set of a dynamical system generated by a differential equation on a Hilbert manifold. As an example, the well-known sine-Gordon equation is considered. In addition, we propose an algorithm for the Whitney stratification of semianalytic sets on finite-dimensional manifolds.",
author = "Kruk, {A. V.} and Malykh, {A. E.} and V. Reitmann",
note = "Funding Information: This work was supported by the Russian Science Foundation under grant no. 14-21-00041 by the German Academic Exchange Service (DAAD). Publisher Copyright: {\textcopyright} 2017, Pleiades Publishing, Ltd. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2017",
month = dec,
day = "1",
doi = "10.1134/S0012266117130031",
language = "English",
volume = "53",
pages = "1715--1733",
journal = "Differential Equations",
issn = "0012-2661",
publisher = "Pleiades Publishing",
number = "13",

}

RIS

TY - JOUR

T1 - Upper Bounds for the Hausdorff Dimension and Stratification of an Invariant Set of an Evolution System on a Hilbert Manifold

AU - Kruk, A. V.

AU - Malykh, A. E.

AU - Reitmann, V.

N1 - Funding Information: This work was supported by the Russian Science Foundation under grant no. 14-21-00041 by the German Academic Exchange Service (DAAD). Publisher Copyright: © 2017, Pleiades Publishing, Ltd. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2017/12/1

Y1 - 2017/12/1

N2 - We prove a generalization of the well-known Douady–Oesterlé theorem on the upper bound for the Hausdorff dimension of an invariant set of a finite-dimensional mapping to the case of a smooth mapping generating a dynamical system on an infinite-dimensional Hilbert manifold. A similar estimate is given for the invariant set of a dynamical system generated by a differential equation on a Hilbert manifold. As an example, the well-known sine-Gordon equation is considered. In addition, we propose an algorithm for the Whitney stratification of semianalytic sets on finite-dimensional manifolds.

AB - We prove a generalization of the well-known Douady–Oesterlé theorem on the upper bound for the Hausdorff dimension of an invariant set of a finite-dimensional mapping to the case of a smooth mapping generating a dynamical system on an infinite-dimensional Hilbert manifold. A similar estimate is given for the invariant set of a dynamical system generated by a differential equation on a Hilbert manifold. As an example, the well-known sine-Gordon equation is considered. In addition, we propose an algorithm for the Whitney stratification of semianalytic sets on finite-dimensional manifolds.

UR - http://www.scopus.com/inward/record.url?scp=85044100578&partnerID=8YFLogxK

U2 - 10.1134/S0012266117130031

DO - 10.1134/S0012266117130031

M3 - Article

AN - SCOPUS:85044100578

VL - 53

SP - 1715

EP - 1733

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 13

ER -

ID: 73406055