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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)

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.
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

12 p, 750.6 KB

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