The initial ensemble dependence of statistical laws in non-hyperbolic dynamical systems with infinite ergodicity are studied by use of the modified 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 Lμ 1-class function. Next, we study the correlation function, which is not an Lμ 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.
|Number of pages
|Journal of the Korean Physical Society
|Published - 2007 Jan
- Ergodic theory
- Non-stationary chaos
ASJC Scopus subject areas
- General Physics and Astronomy