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

Jaume Llibre, RADU SAGHIN , Xiang Zhang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)531-537
Number of pages7
JournalProceedings of the American Mathematical Society
Volume142
Issue number2
StatePublished - 1 Jan 2014

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