DYNAMICAL ASPECTS OF CHAOTIC DYNAMICAL-SYSTEMS JUST AFTER BAND CRISES

Dynamical aspects of chaotic dynamical systems just after the three ba nd crises are studied by extracting various correlations of dynamical systems. Chaotic systems have both periodic and non-periodic motions o f phase points just after the band crises. We decompose the behavior o f phase points for dissipative systems into the motions in the three-b and attractor and in the repeller. Logistic map and Henon map are stud ied as examples of low-dimensional chaotic maps. Driven damped pendulu m is taken up its an example of nonlinear ordinary differential equati ons. Every system exhibits the three-period motion when the local Lyap unov exponent is small and does the non-periodic behavior when the loc al Lyapunov exponent is large. The generalized power spectrum is used for analyzing the behavior of trajectories. We will analyze the interm ittent switching between periodic and non-periodic behaviors by the ge neralized power spectrum in these dissipative systems. This behavior c annot be found directly only by looking at the thermodynamic functions defined in the frame of the thermodynamic formalism. It is shown that the peculiar behaviors of trajectories in the repeller is clearly ext racted.