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

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:

Document Type: Article
MSC: 37B25, 58F10, 70H14
Language: English

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
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\crossref{https://doi.org/10.17323/1609-4514-2018-18-4-681-692}
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