Iterative techniques for computing the linearized manifolds of quasiperiodic tori.
We develop an iterative technique for computing the unstable and stable eigenfunctions of the invariant tori of diffeomorphisms. Using the approach of Jorba [Nonlinearity 14, 943 (2001)], the linearized equations are rewritten as a generalized eigenvalue problem. Casting the system in this light allows us to take advantage of the speed of eigenvalue solvers and create an efficient method for finding the first-order approximations to the invariant manifolds of the torus. We present a numerical scheme based on the power method that can be used to determine the behavior normal to such tori, and give some examples of the application of the method. We confirm the qualitative conclusions of the Melnikov calculations of Lomeli and Meiss [Nonlinearity 16, 1573 (2003)] for a volume-preserving mapping.
Wysham
Derin B
DB
University of Colorado at Boulder, Applied Mathematics, Boulder, Colorado 80309-0526, USA.
Meiss
James D
JD