On the analytic integrability of the 5–dimensional Lorenz system for the gravity–wave activity
For the 5-dimensional Lorenz system
dU/dT = −V W + b V Z,
dV /dT = UW − b UZ,
dW/dT = −UV,
dX/dT = −Z,
dZ/dT = bUV + X
(with ∈ 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.
Autores: Llibre, J., Saghin, R., Zhang, X.
Journal: Proceedings of the american mathematical society
Journal Volume: 142
Journal Issue: 2
Journal Page: 531–537
Tipo de publicación: ISI
Fecha de publicación: 2014
Topics: Analytic first integral, 5–dimensional Lorenz system