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# 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

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