Invariant Manifolds for Quasiperiodic Orbits: The Problem of Reducibility

Jim Meiss

Near a fixed point, a flow can be approximated by a linear, constant coefficient system of ode's--just about the easiest dynamical system of all. Near a periodic orbit, a similar analysis leads to a linear system with periodic coefficients. Here the Floquet theorem applies, and the dynamics of the return map is approximated as a constant, linear map. When the orbit is quasiperiodic, however, linearization of a dynamical system gives a quasiperiodically forced linear system. The existence of Floquet-like exponents depends upon the "reducibility" of these equations. In this talk we will explain what reducibility is, and how one might develop numerical techniques to find invariant manifolds for such systems.