Abstract: This paper presents a method for computing validated error bounds on the
truncation error associated with the linear approximation of an (un)stable invariant manifold
by its eigenspace. The method is based on studying a certain functional equation which
describes a chart map for the invariant manifold. The truncation error is represented as a
bounded analytic function on an explicitly given neighborhood. Moreover studying this
functional equation leads to a method for bounding derivatives of the truncation error as
well. The methods developed in the present work are well suited for studying higher
dimensional invariant manifolds, and validated numerical results are provided for manifolds
of dimension up to one hundred. As an application of these ideas we present some computer
assisted proofs of transverse homoclinic connecting orbits.
Author:
Jason D. Mireles-James
Preprint:
.
An earlier preprint is available here.
Computer Assisted Proof Codes:
(codes require the IntLab package)