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Pàgina inicial > Articles > Articles publicats > The Completely Integrable Differential Systems are Essentially Linear Differential Systems |
Títol variant: | The Completely Integrable Differential Systems are Essentially Linear |
Data: | 2015 |
Resum: | 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. |
Ajuts: | 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 |
Nota: | El títol de la versió pre-print de l'article és: The Completely Integrable Differential Systems are Essentially Linear |
Nota: | 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. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Completely integrability ; Differential systems ; Jacobian multiplier ; Normal form ; Orbital equivalence ; Polynomial differential systems |
Publicat a: | Journal of Nonlinear Science, Vol. 25 Núm. 4 (2015) , p. 815-826, ISSN 1432-1467 |
Postprint 12 p, 750.6 KB |