The q-Phase Transition and Critical Scaling Laws near the Band-Crisis Point of Chaotic Attractors : General and Mathematical Physics

概要

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On the basis of the statistical-mechanical formalism, the q-phase transition for the fluctuation spectrum of coarse-grained local expansion rates of nearby orbits is rigorously derived at the band-crisis point when approached from above, and the critical scaling laws in the vicinity of the crisis point are presented. The implications and the nature of the q-phase transition are thus explained, the difference from the usual phase transitions in thermal equilibrium systems being pointed out. As a solvable model, the asymmetric tent map is adopted and sequences of control parameters which satisfy the Markov condition are considered to use Fujisaka and Inoue's method for the calculation of the fluctuation spectrum. The q-phase transition is of the first order at the band-crisis point, which occurs between the two phases, the multiple-band attractor and the repeller surviving after a partial destruction of the former attractor. The scaling laws near the crisis point are those which reflect the discontinuous change in the local expansion rate at the crisis point.
理論物理学刊行会の論文
1989-11-25