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

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A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems. / Leonov, G. A.; Kuznetsov, N. V.; Kudryashova, E. V.

In: Proceedings of the Steklov Institute of Mathematics, Vol. 272, No. SUPPL. 1, 04.2011, p. S119-S126.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{f654ffc70a534c87a0c5c47ce208e5e1,

title = "A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems",

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 Li{\'e}nard system are written.",

keywords = "limit cycle, Lyapunov quantities, symbolic computations",

author = "Leonov, {G. A.} and Kuznetsov, {N. V.} and Kudryashova, {E. V.}",

note = "Funding Information: This work was partially supported by the Council on Grants of the President of the Russian Federation, by the Federal Target Program “Research and Academic Human Resources of Innovative Russia” (2009–2013), and by the Program of the Federal Education Agency “Development of the Scientific Potential of Higher Schools” (2009–2010).",

year = "2011",

month = apr,

doi = "10.1134/S008154381102009X",

language = "English",

volume = "272",

pages = "S119--S126",

journal = "Proceedings of the Steklov Institute of Mathematics",

issn = "0081-5438",

publisher = "МАИК {"}Наука/Интерпериодика{"}",

number = "SUPPL. 1",

}

RIS

TY - JOUR

T1 - A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

AU - Kudryashova, E. V.

N1 - Funding Information: This work was partially supported by the Council on Grants of the President of the Russian Federation, by the Federal Target Program “Research and Academic Human Resources of Innovative Russia” (2009–2013), and by the Program of the Federal Education Agency “Development of the Scientific Potential of Higher Schools” (2009–2010).

PY - 2011/4

Y1 - 2011/4

N2 - 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.

AB - 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.

KW - limit cycle

KW - Lyapunov quantities

KW - symbolic computations

UR - http://www.scopus.com/inward/record.url?scp=79954574502&partnerID=8YFLogxK

U2 - 10.1134/S008154381102009X

DO - 10.1134/S008154381102009X

M3 - Article

VL - 272

SP - S119-S126

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

SN - 0081-5438

IS - SUPPL. 1

ER -

ID: 5097879