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 $ζ>1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the generalized Lyapunov coefficients $λ_{q}$ 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.