Detection of Cycles without a Center in an ODE In my classes in dynamical systems theory, we were taught how to detect cycles or cyclic behavior in an ODE (be it dampened, sustained or growing) around a fixed point by looking at the eigenvalues for that point (their imaginary component in particular).
But in higher dimensional systems cycles need not have a center, and in practice one often does not even always know the location of a center even if it exists.
Are there any non-local techniques for identifying cyclic behavior in an ODE which would allow me to detect a cycle without a center? Would such techniques similarly allow me to identify strange attractors?

This is a very nontrivial problem in general: to analyze limit cycles in systems of dimension $d\geq 3$. Still there is a lot of research in this direction. A great source of various material is Periodic Motions by Miklos Farkas.
