A note on the first integrals of the ABC system
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)

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

DOI: 10.1063/1.3682692

Postprint 8 p, 676.1 KB

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