Professor Johnson will study linear differential operators with bounded but non-decaying coefficients (which might be almost periodic or paths of an ergodic process). Using techniques from dynamical systems theory, he will study spectral properties and generalized Floquet exponents for such operators. He will apply his results in the following areas: bifurcation from invariant tori in non-linear dynamical systems; spectral properties of the one-dimensional almost periodic Schroedinger operator; linear optimal control theory; the topological index theory of non- periodic ordinary and partial differential equations, and its relation with cohomology theory of certain C* algebras; the Korteweg-deVries equation with bounded initial data. Johnson's research in differential equations is very broadly based and has implications for a variety of fields ranging from pure mathematics to physics and engineering.
