A Reduced Form for Linear Differential Systems and its Application to Integrability of Hamiltonian Systems

Details A Reduced Form for Linear Differential Systems and its Application to Integrability of Hamiltonian Systems A Reduced Form for Linear Differential Systems and its Application to Integrability of Hamiltonian Systems

2009-12-17

arxiv.org/abs/0912.3538v3

Mathematics

Classical Analysis and ODEs

28 pages

Scientific paper

Let $[A]: Y'=AY$ with $A\in \mathrm{M}_n (k)$ be a differential linear system. We say that a matrix $R\in {\cal M}_{n}(\bar{k})$ is a {\em reduced form} of $[A]$ if $R\in \mathfrak{g}(\bar{k})$ and there exists $P\in GL_n (\bar{k})$ such that $R=P^{-1}(AP-P')\in \mathfrak{g}(\bar{k})$. Such a form is often the sparsest possible attainable through gauge transformations without introducing new transcendants. In this article, we discuss how to compute reduced forms of some symplectic differential systems, arising as variational equations of hamiltonian systems. We use this to give an effective form of the Morales-Ramis theorem on (non)-integrability of Hamiltonian systems.

Affiliated with

Also associated with

No associations

Rating

A Reduced Form for Linear Differential Systems and its Application to Integrability of Hamiltonian Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Reduced Form for Linear Differential Systems and its Application to Integrability of Hamiltonian Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Reduced Form for Linear Differential Systems and its Application to Integrability of Hamiltonian Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-348704