The Chaotic Hypothesis for attractors

Let $F$ be a smooth vector field on $\mathbf{R}^3$ generating a chaotic attractor $A$. Two flows are orbitally equivalent when their trajectories correspond up to a reparametrization of time. Chaotic Hypothesis. The flow around $A$ is orbitally equivalent to that of a hyperbolic flow. The hypothesis is presented as a model for studying statistical dynamics near chaotic attractors via an SRB measure; the source notes that existence of such a measure is not known without hyperbolicity assumptions.