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Analytical analysis of a Nose–Hoover generator

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Abstract

It is shown that almost all trajectories of the Nose–Hoover generator have ω-limiting point and the local Lyapunov dimension is three.

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References

  1. A. A. Andronov, A. A. Vitt, and S. E. Haikin, Theorie der Schwingungen (Akad. Verlag, Berlin, 1965).

    Google Scholar 

  2. L. Cezari, Asymptotic Behavior and Stability Problems in Ordinary Differential Equation (Springer, Berlin, 1959).

    Book  Google Scholar 

  3. S. Lefschetz, Differential Equations: Geometric Theory (Intersci. Publ., N.Y., 1957).

    MATH  Google Scholar 

  4. S. Nose, Mol. Phys. 52 (2), 255 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  5. W. Hoover, Phys. Rev. A 31, 1695 (1985).

    Article  ADS  Google Scholar 

  6. J. Sprott, W. Hoover, and C. Hoover, Phys. Rev. E 89, 042914 (2014).

    Article  ADS  Google Scholar 

  7. G. A. Leonov, N. V. Kuznetsov, and T. N. Mokaev, Europ. Phys. J. Spec. Topics 224, 1421 (2015).

    Article  ADS  Google Scholar 

  8. N. V. Kuznetsov and G. A. Leonov, IFAC World Congress 19 (1), 3182 (2014).

    MathSciNet  Google Scholar 

  9. S. Jafari, J. C. Sprott, and M. R. H. Colpayegani, Phys. Lett. A 377, 699 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  10. L. Wang and X. S. Yang, Europ. Phys. J. B 88, 78 (2015).

    Article  ADS  Google Scholar 

  11. V. A. Boichenko, G. A. Leonov, and V. Reitmann, Dimension Theory for Ordinary Differential Equations (Teubner, Wiesbaden, 2005).

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, 199178, Russia

    G. A. Leonov

  2. St. Petersburg State University, St. Petersburg, 199164, Russia

    G. A. Leonov

Authors
  1. G. A. Leonov
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Correspondence to G. A. Leonov.

Additional information

Original Russian Text © G.A. Leonov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 469, No. 1, pp. 51–53.

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Leonov, G.A. Analytical analysis of a Nose–Hoover generator. Dokl. Phys. 61, 340–342 (2016). https://doi.org/10.1134/S1028335816070041

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  • DOI: https://doi.org/10.1134/S1028335816070041

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