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| Pàgina inicial > Articles > Articles publicats > On the integrability of the 5-dimensional Lorenz system for the gravity-wave activity |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universidade de Lisboa. Departamento de Matemàtica)| Data: | 2017 |
| Resum: | We consider the 5-dimensional Lorenz system \[ U' &= -V W b V Z, \\ V' &= UW-b UZ, \\ W'&= -U V,\\ X' &= -Z, \\ Z'&=b UV X \] where b \R \0\ and the derivative is with respect to T. This system describes coupled Rosby waves and gravity waves. First we prove that the number of functionally independent global analytic first integrals of this differential system is two. This solves an open question in the paper On the analytic integrability of the 5-dimensional Lorenz system for the gravity-wave activity, Proc. Amer. Math. Soc. 142 (2014), 531--537, where it was proved that this number was two or three. Moreover, we characterize all the invariant algebraic surfaces of the system, and additionally we show that it has only two functionally independent Darboux first integrals. |
| Ajuts: | Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P |
| Nota: | Agraïments: The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013 |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Matèria: | Darboux first integrals ; Darboux polynomials ; Exponential factors ; Hamiltonian systems ; Polynomial integrability ; Rational integrability ; Weight-homogenous differential systems |
| Publicat a: | Proceedings of the American Mathematical Society, Vol. 145 Núm. 2 (2017) , p. 665-679, ISSN 1088-6826 |
14 p, 708.3 KB |
