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 -