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Mosc. Math. J., 2018, Volume 18, Number 4, Pages 681–692 (Mi mmj679)  

This article is cited in 2 scientific papers (total in 2 papers)

Instability, asymptotic trajectories and dimension of the phase space

V. V. Kozlova, D. V. Treschevab

a Steklov Mathematics Institute, 8 Gubkina street, 11991, Moscow, Russia
b Lomonosov Moscow State University

Abstract: Suppose the origin $x=0$ is a Lyapunov unstable equilibrium position for a flow in $\mathbb{R}^n$. Is it true that there always exists a solution $t\mapsto x(t)$, $x(t)\ne 0$ asymptotic to the equilibrium: $x(t)\to 0$ as $t\to -\infty$? The answer to this and similar questions depends on some details including the parity of $n$ and the class of smoothness of the system. We give partial answers to such questions and present some conjectures.

Key words and phrases: Laypunov stability, asymtotic trajectories, quasihomogeneous systems.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00887
Ministry of Science and Higher Education of the Russian Federation 1.12873.2018/12.1
The second named author was supported by RFBR grant 18-01-00887 and the State Programme of the Ministry of Education and Science of the Russian Federation, project 1.12873.2018/12.1.


DOI: https://doi.org/10.17323/1609-4514-2018-18-4-681-692

Full text: http://www.mathjournals.org/.../2018-018-004-005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 37B25, 58F10, 70H14
Language:

Citation: V. V. Kozlov, D. V. Treschev, “Instability, asymptotic trajectories and dimension of the phase space”, Mosc. Math. J., 18:4 (2018), 681–692

Citation in format AMSBIB
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\by V.~V.~Kozlov, D.~V.~Treschev
\paper Instability, asymptotic trajectories and dimension of the phase space
\jour Mosc. Math.~J.
\yr 2018
\vol 18
\issue 4
\pages 681--692
\mathnet{http://mi.mathnet.ru/mmj679}
\crossref{https://doi.org/10.17323/1609-4514-2018-18-4-681-692}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85060391482}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Kozlov, “First integrals and asymptotic trajectories”, Sb. Math., 211:1 (2020), 29–54  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. P. Palamodov, “On inversion of the Lagrange–Dirichlet theorem and instability of conservative systems”, Russian Math. Surveys, 75:3 (2020), 495–508  mathnet  crossref  crossref  mathscinet  isi  elib
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