Abstract.
We investigate the scaling properties of Lyapunov eigenvectors and exponents in coupled-map lattices exhibiting space-time chaos. A deep interrelation between spatiotemporal chaos and kinetic roughening of surfaces is postulated. We show that the logarithm of unstable eigenvectors exhibits scale-invariance with roughness exponents that can be predicted by a simple scaling conjecture. We argue that these scaling properties should be generic in spatially homogeneous extended systems with local diffusive-like couplings.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.-P. Eckmann, D. Ruelle, Rev. Mod. Phys. 57, 617 (1985)
T. Bohr, M.H. Jensen, G. Paladin, A. Vulpiani, Dynamical Systems Approach to Turbulence (Cambridge University Press, Cambridge, 1998)
A. Pikovsky, J. Kurths, Phys. Rev. E 49, 898 (1994)
A. Pikovsky, A. Politi, Nonlinearity 11, 1049 (1998)
A. Pikovsky, A. Politi, Phys. Rev. E 63, 036207 (2001)
J.M. López, C. Primo, M.A. Rodríguez, I.G. Szendro, Phys. Rev. E 70, 056224 (2004)
A.D. Sánchez, J.M. López, M.A. Rodríguez, M.A. Matías, Phys. Rev. Lett. 92, 204101 (2004)
M. Kardar, G. Parisi, Y.C. Zhang, Phys. Rev. Lett. 56, 889 (1986)
E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge 1994)
R. Carretero-González et al., Chaos 9, 466 (1999)
T. Bohr, G. Grinstein, C. Jayaprakash, Chaos 5, 412 (1995)
V. Oseledec, Trans. Moscow. Math. Soc. 19, 197 (1968)
I. Goldhirsch, P.-L. Sulem, S.A. Orzarg, Physica D 27, 311 (1987)
E.N. Lorenz, Proc. Seminar on Predictability (ECMRWF, Reading UK 1996) 1-18
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Szendro, I., López, J. Scaling properties of spatially extended chaotic systems. Eur. Phys. J. Spec. Top. 143, 13–18 (2007). https://doi.org/10.1140/epjst/e2007-00065-3
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2007-00065-3