On the analytic integrability of the 5–dimensional Lorenz system for the gravity–wave activity

Resumen

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

DOI: 10.1090/S0002-9939-2013-11773-9

URL de la publicación: http://www.ams.org/journals/proc/2014-142-02/S0002-9939-2013-11773-9/S0002-9939-2013-11773-9.pdf