Prog. Theor. Phys. Vol. 76 No. 2 (1986) pp. 335-355
Phase Description Method to Time Averages in the Lorenz System
Department of Physics, Osaka Kyoiku University, Osaka 543
(Received March 5, 1986)
On the basis of the transformation to the rotating coordinates associated with the imbedded unstable limit cycles in the Lorenz system, we present a new representation for the long time averages, which may be applicable to any three-dimensional dissipative dynamical systems producing chaos. By employing the dynamics of the phases of the imbeddid limit cycles, we show that the time average is expressible in terms of two types of the weight factors; the residence time probability density and the factor inbersely proportional to the speed of the phase.
DOI : 10.1143/PTP.76.335
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Citing Article(s) :
Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1057-1076
Phase Description Method to Time Average in Dissipative Chaos
Progress of Theoretical Physics Vol. 80 No. 2 (1988) pp. 216-231
Phase Description Method to Invariant Densities in 1-D Difference Systems