Skip to main content
SpringerLink
Log in

Dynamics of Hamiltonian systems under piecewise linear forcing

  • Statistical, Nonlinear, and Soft Matter Physics
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

A two-parameter family of smooth Hamiltonian systems perturbed by a piecewise linear force is analyzed. The systems are represented both as maps and as dynamical systems. Currently available analytical and numerical results concerning the onset of chaos and global diffusion in such systems are reviewed. Dynamical behavior that has no analogs in the class of systems with analytic Hamiltonians is described. A comparison with the well-studied dynamics of a driven pendulum is presented, and essential differences in dynamics between smooth and analytic systems are highlighted.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. V. Chirikov, Phys. Rep. 52, 263 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  2. A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics, 2nd ed. (Springer, Berlin, 1992).

    Google Scholar 

  3. G. M. Zaslavskii and R. Z. Sagdeev, Introduction to Nonlinear Physics (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  4. B. V. Chirikov, Chaos, Solitons and Fractals 1, 79 (1991).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. J. Moser, Stable and Random Motion in Dynamical Systems (Princeton Univ. Press, Princeton, 1973).

    Google Scholar 

  6. B. V. Chirikov, E. Keil, and A. Sessler, J. Stat. Phys. 3, 307 (1971).

    Article  Google Scholar 

  7. M. Hénon and J. Wisdom, Physica D (Amsterdam) 8, 157 (1983).

    ADS  Google Scholar 

  8. S. Bullett, Commun. Math. Phys. 107, 241 (1986).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  9. M. Wojtkowski, Commun. Math. Phys. 80, 453 (1981); Ergodic Theory Dyn. Syst. 2, 525 (1982).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  10. L. V. Ovsyannikov, private communication (1999).

  11. V. V. Vecheslavov, Preprint No. 99-69, IYaF SO RAN (Inst. of Nuclear Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 1999).

  12. V. V. Vecheslavov, Preprint No. 2000-27, IYaF SO RAN (Inst. of Nuclear Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 2000); nlin.CD/0005048.

  13. V. V. Vecheslavov, Zh. Éksp. Teor. Fiz. 119, 853 (2001) [JETP 92, 744 (2001)].

    Google Scholar 

  14. V. V. Vecheslavov and B. V. Chirikov, Zh. Éksp. Teor. Fiz. 120, 740 (2001) [JETP 93, 649 (2001)].

    Google Scholar 

  15. V. V. Vecheslavov and B. V. Chirikov, Zh. Éksp. Teor. Fiz. 122, 175 (2002) [JETP 95, 154 (2002)].

    MathSciNet  Google Scholar 

  16. B. V. Chirikov and V. V. Vecheslavov, Zh. Éksp. Teor. Fiz. 122, 647 (2002) [JETP 95, 560 (2002)].

    Google Scholar 

  17. V. V. Vecheslavov, Zh. Tekh. Fiz. 73(9), 1 (2003) [Tech. Phys. 48, 1079 (2003)].

    Google Scholar 

  18. V. V. Vecheslavov, Zh. Tekh. Fiz. 74(5), 1 (2004) [Tech. Phys. 49, 521 (2004)].

    Google Scholar 

  19. V. V. Vecheslavov, Zh. Tekh. Fiz. 72(2), 20 (2002) [Tech. Phys. 47, 160 (2002)].

    Google Scholar 

  20. V. V. Vecheslavov, Zh. Tekh. Fiz. 58(1), 20 (1988) [Sov. Phys. Tech. Phys. 33, 11 (1988)].

    Google Scholar 

  21. V. V. Vecheslavov, Zh. Éksp. Teor. Fiz. 125, 399 (2004) [JETP 98, 352 (2004)].

    Google Scholar 

  22. V. V. Vecheslavov, Zh. Éksp. Teor. Fiz. 109, 2208 (1996) [JETP 82, 1190 (1996)].

    Google Scholar 

  23. V. V. Vecheslavov, Pis’ma Zh. Éksp. Teor. Fiz. 63, 989 (1996) [JETP Lett. 63, 1047 (1996)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Budker Institute of Nuclear Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    V. V. Vecheslavov

Authors
  1. V. V. Vecheslavov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, Vol. 127, No. 4, 2005, pp. 915–924.

Original Russian Text Copyright © 2005 by Vecheslavov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vecheslavov, V.V. Dynamics of Hamiltonian systems under piecewise linear forcing. J. Exp. Theor. Phys. 100, 811–819 (2005). https://doi.org/10.1134/1.1926442

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/1.1926442

Keywords

Search

Navigation