Research Summary and Plans

Since my graduate work and throughout my postdoctoral career, I have been interested in hyperbolic dynamical systems, more precisely Anosov flows. Roughly speaking, a smooth flow ft on a closed Riemannian manifold M is called Anosov if the tangent bundle of M splits into three continuous sub-bundles, TM = E⊕E⊕E, such that E is tangent to the flow direction, E is exponentially contracted and E is exponentially expanded by the derivative of ft, for t > 0 (Fig. 1). In other words, an Anosov flow is globally uniformly hyperbolic. If E or E is 1-dimensional, the Anosov flow is called of codimension one.