Non-integrability of Hamiltonian systems through high order variational equations: Summary of results and examples |
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Authors: | R Martínez C Simó |
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Institution: | (1) Dept. de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain;(2) Dept. de Matemàtica Aplicada i Anàlisi, Univ. de Barcelona, Gran Via 585, 08007 Barcelona, Spain |
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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.
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Keywords: | non-integrability criteria differential Galois theory higher order variationals spring-pendulum system |
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