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Pàgina inicial > Articles > Articles publicats > A note on the first integrals of the ABC system |
Data: | 2012 |
Resum: | Without loss of generality the ABC systems reduce to two cases: either A = 0 and B, C ≥ 0, or A = 1 and 0 < B, C ≤ 1. In the first case it is known that the ABC system is completely integrable, here we provide its explicit first integrals. In the second case Ziglin in [14] proved that the ABC system with 0 < B < 1 and C > 0 sufficiently small has no real meromorphic first integrals. We improve Ziglin's result showing that there are no C1 first integrals under convenient assumptions. |
Ajuts: | Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Nota: | Paper selected to be in Research Highlight Archive for 2012 |
Nota: | Agraïments: The second author has been partially supported by FCT through CAMGDS Lisbon. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | ABC systems ; Integrability ; C1 first integrals |
Publicat a: | Journal of mathematical physics, Vol. 53 (2012) , p. 1-5 (023505), ISSN 1089-7658 |
Postprint 8 p, 676.1 KB |