Home > Articles > Published articles > A note on the first integrals of the ABC system |
Date: | 2012 |
Abstract: | 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. |
Grants: | Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Note: | Paper selected to be in Research Highlight Archive for 2012 |
Note: | Agraïments: The second author has been partially supported by FCT through CAMGDS Lisbon. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | ABC systems ; Integrability ; C1 first integrals |
Published in: | Journal of Mathematical Physics, Vol. 53 (2012) , p. 1-5 (023505), ISSN 1089-7658 |
Postprint 8 p, 676.1 KB |