Per citar aquest document: https://ddd.uab.cat/record/145335
Scopus: 4 cites, Web of Science: 4 cites,
The Completely Integrable Differential Systems are Essentially Linear Differential Systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia (Universidade Técnica de Lisboa. Departamento de Matemática)
Zhang, Xiang (Shanghai Jiaotong University. Department of Mathematics)

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.
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.
Nota: Número d'acord de subvenció MINECO/MTM2008–03437
Nota: Número d'acord de subvenció AGAUR/2014/SGR-568
Nota: Número d'acord de subvenció EC/FP7/2012/316338
Nota: Número d'acord de subvenció EC/FP7/2012/318999
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
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

DOI: 10.1007/s00332-015-9243-z


Preprint
12 p, 750.6 KB

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 Registre creat el 2016-01-12, darrera modificació el 2017-10-14



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