English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $[A]: Y'=AY$ with $A\in \mathrm{M}_n (k)$ be a differential linearsystem. We say that a matrix $R\in {\cal M}_{n}(\bar{k})$ is a {\em reducedform} 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 isoften the sparsest possible attainable through gauge transformations withoutintroducing new transcendants. In this article, we discuss how to computereduced forms of some symplectic differential systems, arising as variationalequations of hamiltonian systems. We use this to give an effective form of theMorales-Ramis theorem on (non)-integrability of Hamiltonian systems.

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