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Dynamics arising persistently in smooth dynamical systems ranges from regulardynamics (periodic, quasiperiodic) to strongly chaotic dynamics (Anosov,uniformly hyperbolic, nonuniformly hyperbolic modelled by Young towers). Thelatter include many classical examples such as Lorenz and H\'enon-likeattractors and enjoy strong statistical properties.  It is natural to conjecture (or at least hope) that most dynamical systemsfall into these two extreme situations. We describe a numerical test for such aconjecture/hope and apply this to the logistic map where the conjecture holdsby a theorem of Lyubich, and to the Lorenz-96 system in 40 dimensions wherethere is no rigorous theory. The numerical outcome is almost identical for both(except for the amount of data required) and provides evidence for the validityof the conjecture.

A test for a conjecture on the nature of attractors for smooth dynamical systems