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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 220, Number 1, Pages 59–73
DOI: https://doi.org/10.4213/tmf10679 (Mi tmf10679) 		 
On the uniqueness problem for a central invariant manifold

A. N. Kulikov

Demidov Yaroslavl State University.Yaroslavl, Russia
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DOI: https://doi.org/10.4213/tmf10679
Abstract: We consider a system of autonomous nonlinear ordinary differential equations for which the existence conditions for an invariant manifold are satisfied in the case where this manifold is central. It is well known that the theorem on the existence of a central invariant manifold cannot be supplemented with the statement of its uniqueness. We obtain sufficient conditions that guarantee the uniqueness of the central invariant manifold.
Keywords: central invariant manifold, existence, uniqueness, asymptotic stability, Lyapunov function.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2024-1442
The work was carried out in the framework of the development program of the regional scientific and educational mathematical center (YarSU) with financial support from the Ministry of Science and Higher Education of the Russian Federation (agreement on the subsidies from the federal budget No. 075-02-2024-1442).
Received: 22.01.2024
Revised: 06.03.2024
Published: 30.06.2024
English version:
Theoretical and Mathematical Physics, 2024, Volume 220, Issue 1, Pages 1110–1121
DOI: https://doi.org/10.1134/S0040577924070055
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. N. Kulikov, “On the uniqueness problem for a central invariant manifold”, TMF, 220:1 (2024), 59–73; Theoret. and Math. Phys., 220:1 (2024), 1110–1121
Citation in format AMSBIB
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