Formal and analytic integrability of the Lorenz system

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

16 Citations (Scopus)


The well-known Lorenz system can be written as ẋ = s (y-x), ẏ = rx-y-xz and ż = -bz + xy. Here, we study the first integrals of the Lorenz system that can be described by formal power series. In particular, if s ≠ 0 and, either b is not a negative rational number, or b is a negative rational number and k1b + k2(1 + s) ≠ 0, for all k1 and k2 non-negative integers with k1 + k2 > 0, then the Lorenz system has no analytic first integrals in a neighbourhood of the origin. © 2005 IOP Publishing Ltd.
Original languageEnglish
Pages (from-to)2681-2686
JournalJournal of Physics A: Mathematical and General
Issue number12
Publication statusPublished - 25 Mar 2005


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