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On asymptotic properties of solutions to weakly nonlinear systems in the neighborhood of a singular point. / Kryzhevich, S. G.

In: Mathematical Notes, Vol. 75, No. 5-6, 01.05.2004, p. 635-643.

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

Harvard

Kryzhevich, SG 2004, 'On asymptotic properties of solutions to weakly nonlinear systems in the neighborhood of a singular point', Mathematical Notes, vol. 75, no. 5-6, pp. 635-643.

APA

Kryzhevich, S. G. (2004). On asymptotic properties of solutions to weakly nonlinear systems in the neighborhood of a singular point. Mathematical Notes, 75(5-6), 635-643.

Vancouver

Kryzhevich SG. On asymptotic properties of solutions to weakly nonlinear systems in the neighborhood of a singular point. Mathematical Notes. 2004 May 1;75(5-6):635-643.

Author

Kryzhevich, S. G. / On asymptotic properties of solutions to weakly nonlinear systems in the neighborhood of a singular point. In: Mathematical Notes. 2004 ; Vol. 75, No. 5-6. pp. 635-643.

BibTeX

@article{894a7ab9f40f496284d4f5926b48b4ec,
title = "On asymptotic properties of solutions to weakly nonlinear systems in the neighborhood of a singular point",
abstract = "In this paper, we consider the class of so-called weakly hyperbolic linear systems, which includes correct and hyperbolic (exponentially-dichotomous) systems. We prove new results generalizing related classical theorems on the conditional stability of solutions. We establish the existence of stable manifolds consisting of points corresponding to the solutions of such systems with negative Lyapunov exponents. We study the behavior of solutions starting outside the stable manifold. The technique used in our paper is similar to that in the theory of hyperbolic systems.",
keywords = "Grobman correctness coefficient, Stability problem, Stable manifold, Weakly nonlinear hyperbolic system",
author = "Kryzhevich, {S. G.}",
year = "2004",
month = may,
day = "1",
language = "English",
volume = "75",
pages = "635--643",
journal = "Mathematical Notes",
issn = "0001-4346",
publisher = "Pleiades Publishing",
number = "5-6",

}

RIS

TY - JOUR

T1 - On asymptotic properties of solutions to weakly nonlinear systems in the neighborhood of a singular point

AU - Kryzhevich, S. G.

PY - 2004/5/1

Y1 - 2004/5/1

N2 - In this paper, we consider the class of so-called weakly hyperbolic linear systems, which includes correct and hyperbolic (exponentially-dichotomous) systems. We prove new results generalizing related classical theorems on the conditional stability of solutions. We establish the existence of stable manifolds consisting of points corresponding to the solutions of such systems with negative Lyapunov exponents. We study the behavior of solutions starting outside the stable manifold. The technique used in our paper is similar to that in the theory of hyperbolic systems.

AB - In this paper, we consider the class of so-called weakly hyperbolic linear systems, which includes correct and hyperbolic (exponentially-dichotomous) systems. We prove new results generalizing related classical theorems on the conditional stability of solutions. We establish the existence of stable manifolds consisting of points corresponding to the solutions of such systems with negative Lyapunov exponents. We study the behavior of solutions starting outside the stable manifold. The technique used in our paper is similar to that in the theory of hyperbolic systems.

KW - Grobman correctness coefficient

KW - Stability problem

KW - Stable manifold

KW - Weakly nonlinear hyperbolic system

UR - http://www.scopus.com/inward/record.url?scp=3042792983&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:3042792983

VL - 75

SP - 635

EP - 643

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 5-6

ER -

ID: 41279506