First integrals of local analytic differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
Walcher, Sebastian (RWTH Aachen(Germany). Lehrstuhl A fur Mathematik)

Date:	2012
Abstract:	We investigate formal and analytic first integrals of local analytic ordinary differential equations near a stationary point. A natural approach is via the Poincaré-Dulac normal forms: If there exists a formal first integral for a system in normal form then it is also a first integral for the semisimple part of the linearization, which may be seen as "conserved" by the normal form. We discuss the maximal setting in which all such first integrals are conserved, and show that all first integrals are conserved for certain classes of reversible systems. Moreover we investigate the case of linearization with zero eigenvalues, and we consider a three-dimensional generalization of the quadratic Dulac-Frommer center problem.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Ministerio de Ciencia e Innovación MTM2009-06973 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Formal first integral ; Normal form ; Center ; Reversible system
Published in:	Bulletin des Sciences Mathematiques, Vol. 136 (2012) , p. 342-359, ISSN 0007-4497

DOI: 10.1016/j.bulsci.2011.10.003

Postprint 15 p, 373.2 KB

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