Skip to main content
Log in

Control Of Chaos In Hamiltonian Systems

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

We present a technique to control chaos in Hamiltonian systems which are close to integrable. By adding a small and simple control term to the perturbation, the system becomes more regular than the original one. We apply this technique to a forced pendulum model and show numerically that the control is able to drastically reduce chaos.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • C. Chandre H. R. Jauslin (2002) ArticleTitle‘Renormalization-group analysis for the transition to chaos in Hamiltonian systems’ Physics Reports 365 1–64 Occurrence Handle10.1016/S0370-1573(01)00094-1

    Article  Google Scholar 

  • Chandre, C., Vittot, M., Elskens, Y., Ciraolo, G. and Pettini, M.: 2004, ‘Controlling chaos in area-preserving maps’, submitted and archived in http://arXiv.org/nlin.CD/0405008.

  • Chen, G. and Dong, X.: 1998, From Chaos to Order, World Scientific, Singapore.

  • G. Ciraolo C. Chandre R. Lima M. Vittot M. Pettini C. Figarella Ph. Ghendrih (2004a) ArticleTitle‘Controlling chaotic transport in a Hamiltonian model of interest to magnetized plasmas’ J.Phys. A: Math. Gen. 37 3589–3597 Occurrence Handle10.1088/0305-4470/37/11/004

    Article  Google Scholar 

  • Ciraolo, G., Briolle, F., Chandre, C., Floriani, E., Lima, R., Vittot, M., Pettini, M., Figarella, C. and Ghendrih, Ph.: 2004b, ‘Control of Hamiltonian chaos as a possible tool to control anomalous transport in fusion plasmas’, Phys. Rev. E 69(4), 056213.

  • G. Gallavotti (1982) ArticleTitle‘A criterion of integrability for perturbed nonresonant harmonic oscillators. ‘‘Wick ordering’’ of the perturbations in classical mechanics and invariance of the frequency spectrum’ Commun. Math. Phys 87 365–383 Occurrence Handle10.1007/BF01206029

    Article  Google Scholar 

  • G. Gallavotti (1985) Classical mechanics and renormalization-group G. Velo A.S. Wightman (Eds) Regular and Chaotic Motions in Dynamical Systems Plenum New York 185–231

    Google Scholar 

  • D. J. Gauthier (2003) ArticleTitle‘Controlling chaos’ Am. J. Phys 71 750–759 Occurrence Handle10.1119/1.1572488

    Article  Google Scholar 

  • G. Gentile V. Mastropietro (1996) ArticleTitle‘Methods for the analysis of the Lindstedt series for KAM tori and renormalizability in classical mechanics’ Rev. Math. Phys 8 393–444 Occurrence Handle10.1142/S0129055X96000135

    Article  Google Scholar 

  • J. Laskar (1999) Introduction to frequency map analysis C. Simò (Eds) Hamiltonian Systems with Three or More Degrees of Freedom, NATO ASI Series Kluwer Academic Publishers Dordrecht 134

    Google Scholar 

  • M. Vittot (2004) ArticleTitle‘Perturbation theory and control in classical or quantum mechanics by an inversion formula’ J. Phys. A: Math. Gen 37 6337–6357 Occurrence Handle10.1088/0305-4470/37/24/011

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ciraolo, G., Chandre, C., Lima, R. et al. Control Of Chaos In Hamiltonian Systems. Celestial Mech Dyn Astr 90, 3–12 (2004). https://doi.org/10.1007/s10569-004-6445-3

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-004-6445-3

Keywords

Navigation