Invariant manifold theory links dynamical systems theory and turbulence phenomena. These research notes develop a theory for the Navier-Stokes equations in bounded and certain unbounded geometries. The treatment is suitable for graduate students and scientists studying chaos and turbulence theory. "Contains a lot of useful information, including much that cannot be found in the standard texts ... well worth the reader's attention." - MathSciNet. AUTHOR: Sivaguru S. Sritharan is Provost and Academic Dean at the Air Force Institute of Technology, located at Ohio's Wright-Patterson Air Force Base. He also serves as the Air Force Institute of Technology's Chief Operating Officer and Chief Academic Officer. He received his Ph.D. in Applied Mathematics from the University of Arizona and was the editor of Optimal Control of Viscous Flow .