Intermittency at critical transitions and aging dynamics at edge of chaos

Abstract

We recall that, at both the intermittency transitions and at the Feigenbaum attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the generalized Lyapunov coefficients ${\lambda }_q$ that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the edge of chaos with the appearance of a special value for the entropic index $q$. 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.

Proceedings of: STATPHYS 2004 - 22nd IUPAP International Conference on Statistical Physics, National Science Seminar Complex, Indian Institute of Science, Bangalore, 4-9 July 2004. Pramana, in press

References in corpus (4)

• Ubiquity of metastable-to-stable crossover in weakly chaotic dynamical systems
• Multifractality and nonextensivity at the edge of chaos of unimodal maps
• Universal glassy dynamics at noise-perturbed onset of chaos. A route to ergodicity breakdown
• Critical fluctuations, intermittent dynamics and Tsallis statistics

Cited by in corpus (1)

• Influence of global correlations on central limit theorems and entropic extensivity