We analyze the fluctuating dynamics at the golden-mean transition to chaos in the critical circle map and find that trajectories within the critical attractor consist of infinite sets of power laws mixed together. We elucidate this structure assisted by known renormalization group (RG) results. Next we proceed to weigh the new findings against Tsallis' entropic and Mori's thermodynamic theoretical schemes and observe behavior to a large extent richer than previously reported. We find that the sensitivity to initial conditions ξt has the form of families of intertwined q-exponentials, of which we determine the q-indexes and the generalized Lyapunov coefficient spectra λq. Further, the dynamics within the critical attractor is found to consist of not one but a collection of Mori's q-phase transitions with a hierarchical structure. The value of Mori's 'thermodynamic field' variable q at each transition corresponds to the same special value for the entropic index q. We discuss the relationship between the two formalisms and indicate the usefulness of the methods involved to determine the universal trajectory scaling function σ and/or the ocurrence and characterization of dynamical phase transitions.PACS numbers: 05.45.Ac, 05.90.+m, 05.10.Cc Recently, rigorous results have been developed [8]-[15] that support the validity of q-statistics (outlined in the next paragraph) for the critical attractors associated with the intermittency and period-doubling routes to chaos, i.e. the tangent bifurcation and the accumulation point of the pitchfork bifurcations, but studies of the same type

Semi-Poisson statistics are shown to be obtained by removing every other number from a random sequence. Retaining every (r+1)th level we obtain a family of sequences, which we call daisy models. Their statistical properties coincide with those of Bogomolny's nearest-neighbor interaction Coulomb gas if the inverse temperature coincides with the integer r. In particular, the case r=2 reproduces closely the statistics of quasioptimal solutions of the traveling salesman problem.

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes. We compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators. The expectation is broadly confirmed, but deviations due to scars are observed.

The distribution of votes of one of the corporate parties in Mexico during elections of 2000, 2003 and 2006 is analyzed. After proper normalization and unfolding, the agreement of the votes distributions with those of daisy models of several ranks is good. These models are generated by retaining each r + 1 level in a sequence which follows a Poisson distribution. Beyond the fact that rank 2 daisy model resembles the distribution of the quasi-optimal distances for the Traveling Salesman Problem, no clear explanation exists for this behavior, but the agreement is not fortuitous and the possibility of a universal phenomena for corporate vote is discussed.