Still in future - periodic orbit theory:

accurate prediction for measurable time-averaged observables for a given wall-bounded shear flow:
the mean frictional drag for the plane Couette flow,
turbulent mixing rates, etc.
 
a detailed qualitative and quantitative description of the geometry of turbulent flows
turbulent vs. laminar basins of attraction
applications to non-local control of such flows

For cogniscenti: relative periodic orbits, partially hyperbolic tori - new trace formulas.