Non-integrability of Hamiltonian systems through high order variational equations: Summary of results and examples

Regina Martínez, Carles Simó

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

This paper deals with non-integrability criteria, based on differential Galois theory and requiring the use of higher order variational equations. A general methodology is presented to deal with these problems. We display a family of Hamiltonian systems which require the use of order k variational equations, for arbitrary values of k, to prove non-integrability. Moreover, using third order variational equations we prove the non-integrability of a non-linear spring-pendulum problem for the values of the parameter that can not be decided using first order variational equations. © Pleiades Publishing, Ltd. 2009.
Original languageEnglish
Pages (from-to)323-348
JournalRegular and Chaotic Dynamics
Volume14
Issue number3
DOIs
Publication statusPublished - 18 Jun 2009

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