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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 1, Pages 119–126 (Mi timm532)  
This article is cited in 17 scientific papers (total in 17 papers)

A direct method for calculating Lyapunov values of two-dimensional dynamical systems

G. A. Leonov, N. V. Kuznetsov, E. V. Kudryashova

Saint-Petersburg State University
Full-text PDF (164 kB) Citations (17)
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Abstract: A direct method is proposed for studying the behavior of two-dimensional dynamical systems in the critical case when the linear part of the system has two purely imaginary eigenvalues. This method allows one to construct approximations to solutions of the system and to the “turn-round” time of the trajectory in the form of a finite series in powers of the initial datum. With the help of symbolic computations and the proposed method, first approximations of a solution are constructed and expressions for the first three Lyapunov quantities of the Liénard system are written.
Keywords: Lyapunov quantities, limit cycle, symbolic computations.
Received: 04.03.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, Volume 272, Issue 1, Pages S119–S126
DOI: https://doi.org/10.1134/S008154381102009X
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: G. A. Leonov, N. V. Kuznetsov, E. V. Kudryashova, “A direct method for calculating Lyapunov values of two-dimensional dynamical systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 1, 2010, 119–126; Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S119–S126
Citation in format AMSBIB
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\paper A direct method for calculating Lyapunov values of two-dimensional dynamical systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 1
\pages 119--126
\mathnet{http://mi.mathnet.ru/timm532}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 272
\issue , suppl. 1
\pages S119--S126
\crossref{https://doi.org/10.1134/S008154381102009X}
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    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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