Parameterization of invariant manifolds for difference equations including discrete Lagrangians
Hector Lomeli
Department of Mathematics, Instituto Tecnológico Autónomo de México
Date and time:
Thursday, March 31, 2011 - 4:30pm
Abstract:
We generalize some notions that have played an important role in dynamics (namely invariant manifolds) to the more general context of difference equations. In particular, we study Lagrangian systems in discrete time. We define invariant manifolds, even if the difference equations can not be transformed in a dynamical system. The results apply to several examples in the Physics literature: the Frenkel-Kontorova model with long-range interactions and the Heisenberg model of spin chains with a perturbation. We use a modification of the parametrization method to show the existence of Lagrangian stable manifolds. This method also leads to efficient algorithms that we present with their implementations. (Joint work with Rafael de la Llave)