Construction of nonlinear quasimodes near elliptic periodic orbits

We generalize to arbitrary manifolds with elliptic periodic geodesics a quasimode construction for the nonlinear Schrödinger equation first discovered by the last author.

► We study the NLS Equation on a compact, Riemannian manifold with a periodic elliptic geodesic. ► We will use Fermi coordinates to construct a nonlinear quasimode as in the work of Thomann. ► We must analyze the metric geometry in a neighborhood of a periodic orbit.