New Asymptotic Law Governing Overall Temporal Correlations in Chaotic Systems
Hirokazu Fujisaka, Hiroshi Shibata · Progress of Theoretical Physics · 1991
A new statistical-physical asymptotic law relevant to explicit correlation in temporal fluctuations generated by chaotic dynamics is found. Homogenizing the ensemble members, we can introduce the order-q power spectrum Iq(ω) in the “thermodynamic” limit, whose poles are proved to be determined by the eigenvalues of the order-q evolution operator Hq previously introduced. It is a natural extension of the conventional power spectrum I(ω)(= Iq=0(ω)), and enables us to study various correlation characteristics by controlling the value of parameter q. This manifests that the intensive variable q governs overall temporal-correlation characteristics as well as the global aspect described by fluctuation-spectrum theory.