Based on the Lyapunov characteristic exponents, the ergodic property of dissipative dynamical systems with a few degrees of freedom is studied numerically by employing, as an example, the Lorenz system. The Lorenz system shows the spectra of (+,0,-) type concerning the 1-dimensional Lyapunov exponents, and the exponents take the same values for orbits starting from almost of all initial points on the attractor.
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Shimada et al. (1979) studied this question.
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