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This paper investigates the utility of the weighted Birkhoff average (WBA)for distinguishing between regular and chaotic orbits of flows, extendingprevious results that applied the WBA to maps. It is shown that the WBA can besuper-convergent for flows when the dynamics and phase space function aresmooth, and the dynamics is conjugate to a rigid rotation with Diophantinerotation vector. The dependence of the accuracy of the average on orbit lengthand width of the weight function width are investigated. In practice, theaverage achieves machine precision of the rotation frequency of quasiperiodicorbits for an integration time of O(10^3) periods. The contrasting, relativelyslow convergence for chaotic trajectories allows an efficient discriminationcriterion. Three example systems are studied: a two-wave Hamiltonian system, aquasiperiodically forced, dissipative system that has a strange attractor withno positive Lyapunov exponents, and a model for magnetic field line flow.

Distinguishing between Regular and Chaotic orbits of Flows by the Weighted Birkhoff Average