Chaos perturbation in terms of cycles

Abstract

The conventional perturbation theory encounters formidable challenges when applied to the quantitative analysis or computation of chaotic systems, due to possibly numerous bifurcations as system parameters vary. In this manuscript, however, based on the cycle expansions formulation we found that the preservation of symbolic dynamics is the key to maintain the analyticity and thus to implement a perturbation computation. Even in the presence of bifurcations, a subset of unstable periodic orbits (UPOs) can be selected to resume the computation, giving rise to new perspectives of treating chaos.