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Prog. Theor. Phys. Vol. 66 No. 4 (1981) pp. 1266-1283

[ Full Text PDF : FREE ACCESS (572K) ]

Time-Correlation Functions of One-Dimensional Transformations

Hazime Mori, Byon-Chyol So and Tomoaki Ose

Department of Physics, Kyushu University 33, Fukuoka 812

(Received May 14, 1981)

Abstract:

Broken line transformations consist of three elementary processes; the staircase processes, the rotation around a fixed point and the hopping between different branches. Their relative weights determine the main feature of the time-correlation function <xn | x0 > of mapping xn= f(xn-1), (n=1, 2, …).
It is shown that <xn | x0 >= <x | \hatHnx >, where \hatH is a linear operator closely related to the Frobenius-Perron operator. Eigenvalues and eigenfunctions of \hatH determine the time-correlation function. By means of this method the time-correlation functions of typical broken line transformations are calculated exactly and their features are clarified in terms of the three elementary processes and unstable periodic orbits.


URL : http://ptp.ipap.jp/link?PTP/66/1266/
DOI : 10.1143/PTP.66.1266

[ Full Text PDF : FREE ACCESS (572K) ] Citation:

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