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Linearised higher variational equations

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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
JournalDiscrete and Continuous Dynamical Systems
Issue number11
Early online date1 May 2014
Publication statusPublished - Nov 2014


  • apr2014_23

    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems following peer review. The definitive publisher-authenticated version Linearised higher variational equations. Simon, S. Nov 2014 In : Discrete and Continuous Dynamical Systems. 34, 11, p. 4827-4854 is available online at:

    Accepted author manuscript (Post-print), 733 KB, PDF document

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