Invariant algebraic surfaces of the Lorenz system

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

57 Citations (Scopus)


In this paper we provide a complete classification of the Darboux invariants, of the irreducible Darboux polynomials, of the rational first integrals and of the algebraic integrability for the classical Lorenz system ẋ = s(y - x), ẏ = rx - y - xz, ż = - bz + xy. In the proofs, we use the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. © 2002 American Institute of Physics.
Original languageEnglish
Pages (from-to)1622-1645
JournalJournal of Mathematical Physics
Issue number3
Publication statusPublished - 1 Mar 2002

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