Analysis of Degenerate Solutions to ODEs with Variational Equations of Higher Order

摘要

We give a definition of variational equations of high order that does not involve infinite dimentional functional spaces and Frechet derivatives. We use instead formal differentiation on a finite dimentional analytical manifold. This technique is used for an analysis of degenerate solutions on families of periodic solutions. We demonstrate that for any degenerate solution there exists a non-degenerate system of boundary value problems that allows to compute this solution with the same accuracy as a generic non-degernerate solution on the family.