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

Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Ergodic theorems, spectral theory, Markov operators (37A30) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Rotation numbers and vectors (37E45)

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