Abstract
We recall that at both the intermittency transitions and the Feigenbaum attractor, in unimodal maps of non-linearity of order ζ > 1, the dynamics rigorously obeys the Tsallis statistics. We account for theq-indices and the generalized Lyapunov coefficients λq that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the onset of chaos with the appearance of a special value for the entropic indexq. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.
Similar content being viewed by others
References
C Tsallis,J. Stat. Phys. 52, 479 (1988)
For recent reviews see,Nonextensive entropy — Interdisciplinary applications edited by M Gell-Mann and C Tsallis (Oxford University Press, New York, 2004), see http://tsallis.cat.cbpf.br/biblio.htm for full bibliography
A Cho,Science 297, 1268 (2002)
V Latora, A Rapisarda and A Robledo,Science 300, 250 (2003)
A Robledo,Physica A314, 437 (2002)
F Baldovin and A Robledo,Europhys. Lett. 60, 518 (2002)
F Baldovin and A Robledo,Phys. Rev. E66, 045104 (2002)
F Baldovin and A Robledo,Phys. Rev. E69, 045202 (2004)
A Robledo,Physica D193, 153 (2004)
A Robledo,Physica A344, 631 (2004)
A Robledo, submitted toMolec. Phys., cond-mat/0504044
E Mayoral and A Robledo,Physica A340, 219 (2004)
A Robledo,Phys. Lett. A328, 467 (2004)
F Baldovin and A Robledo, submitted toPhys. Rev. E., cond-mat/0504033
See, for example, H G Schuster,Deterministic chaos. An introduction, 2nd Revised Edition (VCH Publishers, Weinheim, 1988)
See, for example, P Gaspard and X-J Wang,Proc. Natl. Acad. Sci. USA 85, 4591 (1988)
N G Antoniou, Y F Contoyiannis, F K Diakonos and C G Papadoupoulos,Phys. Rev. Lett. 81, 4289 (1998)
Y F Contoyiannis and F K Diakonos,Phys. Lett. A268, 286 (2000)
N G Antoniou, Y F Contoyiannis and F K Diakonos,Phys. Rev. E62, 3125 (2000)
Y F Contoyiannis, F K Diakonos and A Malakis,Phys. Rev. Lett. 89, 035701 (2002)
G Anania and A Politi,Europhys. Lett. 7 (1988)
H Hata, T Horita and H Mori,Progr. Theor. Phys. 82, 897 (1989)
E Mayoral and A Robledo, submitted toPhys. Rev. E., cond-mat/0501366
J P Crutchfield, J D Farmer and B A Huberman,Phys. Rep. 92, 45 (1982)
J Crutchfield, M Nauenberg and J Rudnick,Phys. Rev. Lett. 46, 933 (1981)
B Shraiman, C E Wayne and P C Martin,Phys. Rev. Lett. 46, 935 (1981)
F Baldovin, L G Moyano, A P Majtey, C Tsallis and A Robledo,Physica A340, 205 (2004)
For a recent review see, P G De Benedetti and F H Stillinger,Nature (London) 410, 267 (2001)
See, for example, J P Bouchaud, L F Cugliandolo, J Kurchan and M Mezard, inSpin glasses and random fields edited by A P Young (World Scientific, Singapore, 1998)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Robledo, A. Intermittency at critical transitions and aging dynamics at the onset of chaos. Pramana - J Phys 64, 947–956 (2005). https://doi.org/10.1007/BF02704156
Issue Date:
DOI: https://doi.org/10.1007/BF02704156
Keywords
- Intermittency
- criticality
- glassy dynamics
- ergodicity breakdown
- onset of chaos
- external noise
- nonextensive statistics