Periodic orbits and non-integrability of generalized classical Yang-Mills Hamiltonian systems
Jiménez-Lara, Lidia (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic). Departamento de Física)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2011
Abstract:	The averaging theory of first order is applied to study a generalized Yang-Mills system with two parameters. Two main results are proved. First, we provide sufficient conditions on the two parameters of the generalized system to guarantee the existence of continuous families of isolated periodic orbits parameterized by the energy, and these families are given up to first order in a small parameter. Second, we prove that for the nonintegrable classical Yang-Mills Hamiltonian systems, in the sense of Liouville-Arnold, which have the isolated periodic orbits found with averaging theory, cannot exist in any second first integral of class C1. This is important because most of the results about integrability deals with analytic or meromorphic integrals of motion.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
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Document:	Article
Published in:	Journal of mathematical physics, Vol. 52 (2011), p. 32901, ISSN 1089-7658

Postprint 23 p, 323.0 KB

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