| Keywords | Chaos, / Intermittent chaos, / Power spectrum, / Coarse-grained local expansion rates, / Anomalous scaling laws, / q-phase transition of chaotic attractors, / Statistical-thermodynamical formalism, / Energy dissipation and its fluctuations in chaos. |
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| Research Abstract |
"Oji Seminar on Non-Linear Non-Equilibrium Statistical Mechanics" was organized by Professor H. Mori (one of the investigators of the present project) and held at Kyoto in 1978 (see Prog. Theor. Phys. Suppl. No. 64 (1978)). Since then the studies of nonlinear dynamics on the basis of dissipative dynamical systems were started and encouraged for Japanese scientists, particularly, physicists, mathematicians, biologists, chemists, engineers, geologists and even for socialists.
Onset of turbulence or the scenario to chaos in dissiparatieve dynamical systems is now known to be classified into a few types, which are the well-known period-doubling route, the collapse of a torus and the intermittency. Prominent properties of chaotic orbits are represented by several scaling laws for spatial and temporal scales and highly coherent behaviors or strong time correlations due to order in chaos.
Our goal is to construct a statistical-dynamical paradigm for chaotic or turbulent motions which gives universal behaviors in nonlinear-nonequilibrium systems. Due to the above guiding priciples, we have performed successfully the following themes :
1) Statistical-physical theory of global spectral structures of type I and III intermittent chaos and the intermittent chaos due to the collapse of period-3 windows.
2) Characterization of local structures of chaotic attractors in terms of coarse-grained local expansion rates, and its spectrum psi (LAMBDA) and q-phase transition.
3) Long-time correlations due to memory effect of critical orbits and its critical scaling laws of local expansion rate spectrum.
4) Advective diffusion and mixing of particles in Hamiltonian dynamical systems.
5) Energy dissipation and its fluctuations in chaotic dynamical systems.
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