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Transient chaos in multidimensional Hamiltonian system with weak dissipation

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Abstract

The dynamics of two coupled twist maps with weak dissipation is studied. The calculation of Lyapunov exponents is used to analyze the structure of the action plane of the system. The chaotic transient dynamics is revealed for extremely small values of dissipation by calculation of finite-time Lyapunov exponents. The stagger-and-step method is used to obtain the chaotic saddle and it is found that it is similar to the Arnold web.

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References

  1. M. Woltering, M. Markus, Phys. Rev. Lett. 84, 630 (2000)

    Article  ADS  Google Scholar 

  2. M. Dhamala, Y.-C. Lai, Phys. Rev. E. 60, 6176 (1999)

    Article  ADS  Google Scholar 

  3. M. Dhamala, Y.-C. Lai, E.J. Kostelich, Phys. Rev. E. 61, 6485 (2000)

    Article  ADS  Google Scholar 

  4. M. Dhamala, Y.C. Lai, Phys. Rev. E 59, 1646 (1999)

    Article  ADS  Google Scholar 

  5. H.W. Yin, J.H. Dai, H.J. Zhang, Phys. Rev. E 54, 371 (1996)

    Article  ADS  Google Scholar 

  6. A. Koronovsky, I. Rempen, D. Trubetskov, A. Hramov, Izvestia akademii nauk seria fizicheskaya 66, 1754 (2002)

    Google Scholar 

  7. L. Chen, K. Aihara, Neural Networks 8, 915 (1995)

    Article  Google Scholar 

  8. P.V. Coveney, A.N. Chaudry, J. Chem. Phys. 97, 7448 (1998)

    Article  ADS  Google Scholar 

  9. R.W. White, Environment and Planning A 22, 1309 (1990)

    Article  Google Scholar 

  10. Y.-C. Lai, K. Zyczkowski, C. Grebogi, Phys. Rev. E 59, 5261 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  11. S. Kraut, U. Feudel, Phys. Rev. 66, 015207 (2002)

    ADS  MathSciNet  Google Scholar 

  12. Y.-C. Lai, T. Tel, Transient Chaos: Complex Dynamics on Finite Time Scales (Springer, New York, 2011), Vol. 173

  13. J.L. Kaplan, J.A. Yorke, Comm. Math. Phys. 67, 93 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  14. L.A. Bunimovich, Nonlinearity 27, 51 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  15. C. Grebogi, E. Ott, J.A. Yorke, Phys. Rev. Lett. 48, 1507 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  16. H. Kantz, P. Grassberger, Physica D 17, 75 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  17. G.H. Hsu, E. Ott, C. Grebogi, Phys. Lett. A 127, 199 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  18. V.I. Arnol’d, Sov. Math. 5, 581 (1964)

    Google Scholar 

  19. G.M. Zaslavsky, R.Z. Sagdeev, D.A. Usikov, A.A. Chernikov, Weak Chaos and Quasi-Regular Patterns (Cambridge University Press, Cambridge, 1991) p. 265

  20. G.M. Zaslavsky, Physics of Chaos in Hamiltonian Dynamics (Imperial College Press, London, 1998) p. 350

  21. A.P. Kuznetsov, A.V. Savin, D.V. Savin, Physica A 387, 1464 (2008)

    Article  ADS  Google Scholar 

  22. A.V. Savin, D.V. Savin, ar**v:1302.5361[nlin.CD]

  23. E.V. Felk, A.P. Kuznetsov, A.V. Savin, Physica A 410, 561 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  24. U. Feudel, C. Grebogi, B.R. Hunt, J.A. Yorke, Phys. Rev. 54, 71 (1996)

    ADS  MathSciNet  Google Scholar 

  25. U. Feudel, C. Grebogi, Phys. Rev. Lett. 91, 134102 (2003)

    Article  ADS  Google Scholar 

  26. M. Tabor, in Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989) p. 364

  27. L.E. Reichl, The Transition to Chaos in Conservative Classical Systems: Quantum Manifestations (Springer-Verlag, Berlin, 1992)

  28. K. Froeschle, E. Lega, M. Guzzo, Mechanics and Dynamical Astronomy 95, 141 (2006)

    Article  ADS  Google Scholar 

  29. M. Guzzo, E. Lega, K. Froeschle, ar**v:nlin/0407059[nlin.CD]

  30. G. Benettin, L. Galgani, J.M. Strelcyn, Phys. Rev. 14, 2338 (1976)

    Article  ADS  Google Scholar 

  31. D. Sweet, H.E. Nusse, J.A. Yorke, Phys. Rev. Lett. 86, 2261 (2001)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Saratov State University, Saratov, Russia

    E. V. Felk, A. V. Savin & A. P. Kuznetsov

  2. Saratov Branch of the Institute of Radio-Engineering and Electronics of RAS, Saratov, Russia

    A. P. Kuznetsov

Authors
  1. E. V. Felk
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  2. A. V. Savin
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  3. A. P. Kuznetsov
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Correspondence to E. V. Felk.

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Felk, E.V., Savin, A.V. & Kuznetsov, A.P. Transient chaos in multidimensional Hamiltonian system with weak dissipation. Eur. Phys. J. Spec. Top. 226, 1777–1784 (2017). https://doi.org/10.1140/epjst/e2017-70025-y

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  • DOI: https://doi.org/10.1140/epjst/e2017-70025-y

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