The Completely Integrable Differential Systems are Essentially Linear Differential Systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade Técnica de Lisboa. Departamento de Matemática)
Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)

Additional title:	The Completely Integrable Differential Systems are Essentially Linear
Date:	2015
Abstract:	Let ˙x = f(x) be a C k autonomous differential system with k ∈ N ∪ {∞, ω} defined in an open subset Ω of R n. Assume that the system ˙x = f(x) is C r completely integrable, i. e. there exist n−1 functionally independent first integrals of class C r with 2 ≤ r ≤ k. If the divergence of system ˙x = f(x) is non-identically zero, then any Jacobian multiplier is functionally independent of the n − 1 first integrals. Moreover the system ˙x = f(x) is C r−1 orbitally equivalent to the linear differential system ˙y = y in a full Lebesgue measure subset of Ω. For Darboux and polynomial integrable polynomial differential systems we characterize their type of Jacobian multipliers.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999
Note:	El títol de la versió pre-print de l'article és: The Completely Integrable Differential Systems are Essentially Linear
Note:	Agraïments: Grant UNAB13-4E-1604, and from the recruitment program of high-end foreign experts of China. The second author is supported by Portuguese national funds through FCT-Fundação para a Ciência e a Tecnologia: Project PEst-OE/EEI/LA0009/2013 (CAMGSD). The third author is partially supported by NNSF of China Grant Number 11271252, by RFDP of Higher Education of China Grant Number 20110073110054 and by innovation program of Shanghai municipal education commission Grant 15ZZ012.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Completely integrability ; Differential systems ; Jacobian multiplier ; Normal form ; Orbital equivalence ; Polynomial differential systems
Published in:	Journal of Nonlinear Science, Vol. 25 Núm. 4 (2015) , p. 815-826, ISSN 1432-1467

DOI: 10.1007/s00332-015-9243-z

Postprint 12 p, 750.6 KB

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