On the integrability of the 5-dimensional Lorenz system for the gravity-wave activity
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemàtica)

Date:	2017
Abstract:	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.
Grants:	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
Note:	Agraïments: The second author is partially supported by FCT/Portugal through UID/MAT/04459/2013
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux first integrals ; Darboux polynomials ; Exponential factors ; Hamiltonian systems ; Polynomial integrability ; Rational integrability ; Weight-homogenous differential systems
Published in:	Proceedings of the American Mathematical Society, Vol. 145 Núm. 2 (2017) , p. 665-679, ISSN 1088-6826

DOI: 10.1090/proc/13233

Postprint 14 p, 708.3 KB

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