Linearised higher variational equations

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Abstract

This work explores the tensor and combinatorial constructs underlying
the linearised higher-order variational equations LVEkψ of a generic autonomous system along a particular solution ψ . The main result of this paper is a compact yet explicit and computationally amenable form for said variational systems and their monodromy matrices. Alternatively, the same methods are useful to retrieve, and sometimes simplify, systems satisfied by the coefficients of the Taylor expansion of a formal first integral for a given dynamical system. This is done in preparation for further results within Ziglin-Morales-Ramis theory, specifically those of a constructive nature.

Original languageEnglish
Pages (from-to)4827-4854
Number of pages28
JournalDiscrete and Continuous Dynamical Systems
Volume34
Issue number11
Early online date1 May 2014
DOIs
Publication statusPublished - 1 Nov 2014

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