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Numerical computation of the Floquet normal form and applications


por el

Dr. Jason D. Mireles-James

Department of Mathematical Sciences, Florida Atlantic University

Resumen:
The Parameterization Method is a functional analytic framework for studying invariant manifolds. I will discuss how it can be used to compute high order Fourier-Taylor expansions of stable/unstable manifolds for periodic orbits of differential equations. In order to apply the method it is first necessary to compute Fourier expansions of the periodic orbit and its stable/unstable bundles. One method for computing the bundles is to exploit the Floquet normal form. Numerical computation of the Floquet form is somewhat expensive, however we find that the form reduces to constant coefficients all of the equations for the higher order jets of the manifold. Then in this situation the overhead is actually worth the cost. I will illustrate the computational method by some examples and discuss how the manifolds are used to compute connecting orbits.

Miércoles 14 de octubre, 2015
18:00 hrs.
Salón 203, Edificio Anexo, IIMAS

Informes: coloquiomym@gmail.com, o al 5622-3564.