Determination of chaotic dynamical correlations in terms of unstable periodic orbits

For low-dimensional chaotic systems, we find that time correlation functions can be accurately approximated by a single unstable periodic orbit. The method of this determination consists of the following two steps. First, the time correlation functions are expanded in terms of static correlation functions by making use of the expansion method recently proposed by one of the authors [H. Fujisaka, Prog. Theor. Phys. 114 (2005), 1]. Second, the static quantities are approximated in terms of an unstable periodic orbit embedded in the strange attractor. Thus the dynamical correlation functions in chaotic systems can be determined in terms of an unstable periodic orbit. Furthermore, applying this method to low-dimensional chaotic models, we prove the usefulness of the present approach.