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New Aspects of the Correlation Functions in Non-Hyperbolic Chaotic Systems
Takuma Akimoto,Yoji Aizawa 한국물리학회 2007 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.50 No.1I
The initial ensemble dependence of statistical laws in non-hyperbolic dynamical systems with in.nite ergodicity are studied by use of the modi.ed Bernoulli maps. We show that statistical laws crucially depend on the initial ensemble and that the time average for the Lyapunov exponent converges in distribution for the non-stationary regime. This is completely consistent with the Darling-Kac-Aaronson (DKA) limit theorem from the fact that the Lyapunov exponent is an L1 ¹- class function. Next, we study the correlation function, which is not an L1 ¹-class function. The most remarkable result is that the transformed correlation function also reveals uniform convergence in distribution in the same sense of the DKA limit theorem.