Abstract
We investigate the structure of the invariant measure of space-time chaos by adopting an “open-system” point of view. We consider large but finite windows of formally infinite one-dimensional lattices and quantify the effect of the interaction with the outer region by mapping the problem on the dynamical characterization of localized perturbations. This latter task is performed by suitably generalizing the concept of Lyapunov spectrum to cope with perturbations that propagate outside the region under investigation. As a result, we are able to introduce a “volume”-propagation velocity, i.e., the velocity with which ensembles of localized perturbations tend to fill volumes in the neighbouring regions.
Similar content being viewed by others
REFERENCES
H. Kantz and T. Schreiber, Nonlinear Time-Series Analysis (Cambridge University Press, 1999).
Y. Pomeau, C. R. Acad. Sci. Paris, t. 300, Série II 7:235 (1985).
L. Bunimovich and Ya. G. Sinai, Nonlinearity 1:491 (1988).
G. Keller and M. Kunzle, Ergodic Theory Dynam. Systems 12:297 (1992).
J. Bricmont and A. Kupiainen, Comm. Math. Phys. 178:703 (1996).
M. Jiang and Ya. B. Pesin, Comm. Math. Phys. 193:675 (1998).
D. Ruelle, Comm. Math. Phys. 87:287 (1982).
P. Manneville, in Macroscopic Modeling of Turbulent Flows, Vol. 230, Lecture Notes in Physics, O. Pironneau ed. (Springer-Verlag, 1985).
P. Grassberger, Phys. Scripta 40:346 (1989).
Ya. G. Sinai, Internat. J. Bifur. Chaos 6:1137 (1996).
D. Dolgopyat, J. Stat. Phys. 86:377 (1997).
P. Collet and J.-P. Eckmann, Comm. Math. Phys. 200:699 (1999).
L. S. Tsimring, Phys. Rev. E 48:3421 (1993).
L. N. Korzinov and M. I. Rabinovich, in Applied Nonlinear Dynamics, Vol. 2 (Saratov University Press, 1994), pp. 59–69.
A. N. Kolmogorov and V. M. Tikhomirov, Selected Works of A. N. Kolmogorov, Vol. III, A. N. Shirayayev, ed. (Dordrecht, Kluwer, 1993).
A. Torcini, A. Politi, G. P. Puccioni, and G. D'Alessandro, Physica D 53:85 (1991).
A. Politi and G. P. Puccioni, Physica D 58:384 (1992).
E. Olbrich, R. Hegger, and H. Kantz, Phys. Lett. A 244:538 (1998).
A. Politi and A. Witt, Phys. Rev. Lett. 82:3034 (1999).
S. V. Zelik, Discrete Contin. Dynam. Systems 7:593 (2001).
S. V. Zelik, Comm. Pure Appl. Math. 56:584 (2003).
J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57:617 (1985).
R. J. Deissler and K. Kaneko, Phys. Lett. A 119:397 (1987).
K. Kaneko, Progr. Theoret. Phys. 72:480 (1984).
I. Waller and R. Kapral, Phys. Rev. A 30:2047 (1984).
A. Politi and A. Torcini, Europhys. Lett. 28:545 (1994).
S. Isola, A. Politi, S. Ruffo, and A. Torcini, Phys. Lett. A 143:365 (1990).
F. Cecconi, R. Livi, and A. Politi, Phys. Rev. E 57:2703 (1998).
P. Cipriani and A. Politi, in preparation.
S. Lepri, A. Politi, and A. Torcini, J. Stat. Phys. 82:1429 (1996).
S. Lepri, A. Politi, and A. Torcini, J. Stat. Phys. 88:31 (1997).
G. Gallavotti, Large Deviations, Fluctuation Theorem and Onsager-Machlup Theory in Non-Equilibrium Statistical Mechanics, preprint FM 2002–03, available on http://ipparco.romal.infn.it.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cipriani, P., Politi, A. An Open-System Approach for the Characterization of Spatio-Temporal Chaos. Journal of Statistical Physics 114, 205–228 (2004). https://doi.org/10.1023/B:JOSS.0000003110.15959.d3
Issue Date:
DOI: https://doi.org/10.1023/B:JOSS.0000003110.15959.d3