Title: Constructing Chaotic Coordinates for non-integrable dynamical systems
Speaker: Dr. Stuart Hudson
Princeton Plasma Physics Laboratory
Abstract: Action-angle coordinates can be constructed for so-called integrable Hamiltonian dynamical systems, for which there exists a foliation of phase space by surfaces that are invariant under the dynamical flow. Perturbations generally destroy integrability. However, we know that periodic orbits will survive, as will cantori, as will the "KAM" surfaces that have sufficiently irrational frequency, depending on the perturbation. There will also be irregular "chaotic" trajectories. By "fitting" the coordinates to the invariant structure that are robust to perturbation, action-angle coordinates may be generalized to non-integrable dynamical systems. These coordinates "capture" the invariant dynamics and neatly partition the chaotic regions. These so-called chaotic coordinates are based on a construction of almost-invariant surfaces known as ghost surfaces. The theoretical definition and numerical construction of ghost surfaces and chaotic coordinates will be described and illustrated.