TY - JOUR

T1 - On the analytic integrability of the 5-dimensional lorenz system for the gravity-wave activity

AU - Llibre, Jaume

AU - Saghin, Radu

AU - Zhang, Xiang

PY - 2014

Y1 - 2014

N2 - For the 5-dimensional Lorenz system dU/dT = -VW + bV Z, dV/dT = UW - bUZ, dW/dT = -UV, dX/dT = -Z, dZ/dT = bUV + X (with b ∈ ℝ a parameter), describing coupled Rosby and gravity waves, we prove that it has at most three functionally independent global analytic first integrals and exactly three functionally independent global analytic first integrals when b = 0. In this last case the system is completely integrable with an additional functionally independent first integral which is not globally analytic.

AB - For the 5-dimensional Lorenz system dU/dT = -VW + bV Z, dV/dT = UW - bUZ, dW/dT = -UV, dX/dT = -Z, dZ/dT = bUV + X (with b ∈ ℝ a parameter), describing coupled Rosby and gravity waves, we prove that it has at most three functionally independent global analytic first integrals and exactly three functionally independent global analytic first integrals when b = 0. In this last case the system is completely integrable with an additional functionally independent first integral which is not globally analytic.

UR - http://www.scopus.com/inward/record.url?scp=84889014989&partnerID=8YFLogxK

U2 - 10.1090/s0002-9939-2013-11773-9

DO - 10.1090/s0002-9939-2013-11773-9

M3 - Article

AN - SCOPUS:84889014989

SN - 0002-9939

VL - 142

SP - 531

EP - 537

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -