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Matematicheskie Zametki, 2010, Volume 88, Issue 2, Pages 275–287
DOI: https://doi.org/10.4213/mzm8805 (Mi mzm8805) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root

V. S. Samovol

State University – Higher School of Economics
Full-text PDF (437 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm8805
Abstract: In this paper, in a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has one zero eigenvalue, while the other eigenvalues lie outside the imaginary axis. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.
Keywords: autonomous system, ordinary differential equations, finitely smooth equivalence, singular point, zero eigenvalue, Taylor series, normal form, $N$-jet of a function.
Received: 17.11.2008
Revised: 26.11.2009
English version:
Mathematical Notes, 2010, Volume 88, Issue 2, Pages 251–261
DOI: https://doi.org/10.1134/S0001434610070230
Bibliographic databases:
Document Type: Article
UDC: 517.91
Language: Russian
Citation: V. S. Samovol, “Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root”, Mat. Zametki, 88:2 (2010), 275–287; Math. Notes, 88:2 (2010), 251–261
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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