Distinguishing between regular and chaotic orbits of flows by the weighted Birkhoff average

This paper investigates the utility of weighted Birkhoff average (WBA) for distinguishing between regular and chaotic orbits flows, extending previous results that applied WBA to maps. It is shown can be super-convergent flows when dynamics phase space function are smooth, conjugate a rigid rotation with Diophantine vector. The dependence accuracy on orbit length width weight investigated. In practice, achieves machine precision frequency quasiperiodic an integration time O(103) periods. contrasting, relatively slow convergence trajectories allows efficient discrimination criterion. Three example systems studied: two-wave Hamiltonian system, quasiperiodically forced, dissipative system has strange attractor no positive Lyapunov exponents, model magnetic field line flow.