Periodic orbits and nonintegrability of generalized classical Yang-Mills Hamiltonian systems
- Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, P.O. Box 55-534, Mexico, D.F., 09340 (Mexico)
- Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia (Spain)
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 C{sup 1}. This is important because most of the results about integrability deals with analytic or meromorphic integrals of motion.
- OSTI ID:
- 21501291
- Journal Information:
- Journal of Mathematical Physics, Vol. 52, Issue 3; Other Information: DOI: 10.1063/1.3559145; (c) 2011 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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