Skip to main content
SpringerLink
Log in

Chronotopic Lyapunov analysis. I. A detailed characterization of 1D systems

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Instabilities in 1D spatially extended systems are studied with the aid of both temporal and spatial Lyapunov exponents. A suitable representation of the spectra allows a compact description of all the possible disturbances in tangent space. The analysis is carried out for chaotic and periodic spatiotemporal patterns. Singularities of the spectra and localization properties of the associated Lyapunov vectors are discussed.

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. D. Ruelle and J.-P. Eckmann,Rev. Mod. Phys. 57:617 (1985).

    Google Scholar 

  2. P. Mannneville,Dissipative Structures and Weak Turbulence (Academic Press, San Diego, 1990).

    Google Scholar 

  3. A. Politi and A. Torcini,Chaos,2:293 (1992).

    Google Scholar 

  4. G. Giacomelli and A. Politi,Europhys. Lett. 15:387 (1991).

    Google Scholar 

  5. R. J. Deissler and K. Kaneko,Phys. Lett. A 119:397 (1987).

    Google Scholar 

  6. A. S. Pikovsky,Chaos 3:225 (1993).

    Google Scholar 

  7. G. Giacomelli, S. Lepri, and A. Politi,Phys. Rev. E 51:3939 (1995).

    Google Scholar 

  8. S. Lepri, A. Politi, and A. Torcini, Chronotopic Lyapunov analysis: (II) Towards a unified approach, unpublished.

  9. S. Isola, A. Politi, S. Ruffo, and A. Torcini,Phys. Lett. A 143:365 (1990).

    Google Scholar 

  10. K. Kaneko,Prog. Theor. Phys. 72:980 (1984).

    Google Scholar 

  11. I. Waller and R. Kapral,Phys. Rev. A 30:2047 (1984).

    Google Scholar 

  12. H. Kantz and P. Grassberger,Phys. Lett. A 123:437 (1987).

    Google Scholar 

  13. M. S. Bourzutschky and M. C. Cross,Chaos 2:173 (1992).

    Google Scholar 

  14. A. S. Pikovsky,Phys. Lett. 137A:121 (1989).

    Google Scholar 

  15. Y. Pomeau, A. Pumir, and P. Pelce,J. Stat. Phys. 37:39 (1984); K. Kaneko,Prog. Theor. Phys. 74:1033 (1984); P. Manneville, inLectures Notes in Physics, Vol. 230 (Springer, Berlin, 1985), p. 319; R. Livi, A. Politi, and S. Ruffo,J. Phys. A 19:2033 (1986).

    Google Scholar 

  16. J.-P. Eckmann and C. E. Wayne,J. Stat. Phys. 50:853 (1988); Ya. Sinai, A remark concerning the thermodynamic limit of the Lyapunov spectrum, Preprint (1995).

    Google Scholar 

  17. P. Grassberger,Physica Scripta 40:346 (1989).

    Google Scholar 

  18. I. Shimada and T. Nagashima,Prog. Theor. Phys. 61:1605 (1979); G. Benettin, L. Galgani, A. Giorgilli, and J. M. Strelcyn,Meccanica 15:21 (1980).

    Google Scholar 

  19. R. Livi, G. Paladin, S. Ruffo, and A. Vulpiani, InAdvances in Phase Transitions and Disorder Phenomena, G. Busiello, L. De Cesare, F. Mancini, and M. Marinaro, eds. (World Scientific, Singapore, 1987).

    Google Scholar 

  20. K. Kaneko,Physica 23D:436 (1986).

    Google Scholar 

  21. E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan,Phys. Rev. Lett. 42:673 (1979).

    Google Scholar 

  22. T. Konishi and K. Kaneko,Phys. Rev. A 40:6130 (1989);J. Phys. A 23:L715 (1990).

    Google Scholar 

  23. J. L. Pichard and G. André,Europhys. Lett. 2:477 (1986).

    Google Scholar 

  24. S. Lepri, A. Politi, and A. Torcini, Fractal features of Lyapunov vectors, unpublished.

  25. F. Izrailev, T. Kottos, A. Politi, and S. Ruffo, unpublished.

  26. H. A. Posch and W. G. Hoover,Phys. Rev. A 38:473 (1988).

    Google Scholar 

  27. A. S. Pikovsky and J. Kurths,Phys. Rev. E 49:898 (1994).

    Google Scholar 

  28. M. Kardar, G. Parisi, and Y. C. Zhang,Phys. Rev. Lett. 56:889 (1986).

    Google Scholar 

  29. T. Bohr, G. Grinstein, and C. Jayaprakash,Chaos 5:412 (1994).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Universitá di Bologna, I-40127, Bologna, Italy

    Stefano Lepri

  2. Istituto Nazionale di Fisica Nucleare, I-40127, Bologna, Italy

    Stefano Lepri

  3. Istituto Nazionale di Ottica and Istituto Nazionale di Fisica Nucleare, I-50125, Firenze, Italy

    Antonio Politi

  4. Theoretische Physik, Bergische Universität-Gesamthochshule Wuppertal, D-42097, Wuppertal, Germany

    Alessandro Torcini

Authors
  1. Stefano Lepri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio Politi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alessandro Torcini
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lepri, S., Politi, A. & Torcini, A. Chronotopic Lyapunov analysis. I. A detailed characterization of 1D systems. J Stat Phys 82, 1429–1452 (1996). https://doi.org/10.1007/BF02183390

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02183390

Key Words

Search

Navigation