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

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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.

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Authors and Affiliations

  1. St. Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034, Russia

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

Authors
  1. G. A. Leonov
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  2. N. V. Kuznetsov
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  3. E. V. Kudryashova
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Correspondence to G. A. Leonov.

Additional information

Original Russian Text © G.A. Leonov, N.V.Kuznetsov, E.V.Kudryashova, 2010, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Vol. 16, No. 1.

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Leonov, G.A., Kuznetsov, N.V. & Kudryashova, E.V. A direct method for calculating Lyapunov quantities of two-dimensional dynamical systems. Proc. Steklov Inst. Math. 272 (Suppl 1), 119–126 (2011). https://doi.org/10.1134/S008154381102009X

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  • DOI: https://doi.org/10.1134/S008154381102009X

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