Darboux integrability for the Rössler system

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)


In this note we characterize all generators of Darboux polynomials of the Rössler system by using weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations. As a corollary we prove that the Rössler system is not algebraically integrable, and that every rational first integral is a rational function in the variable x2+y2+2z. Moreover, we characterize the topological phase portrait of the Darboux integrable Rössler system.
Original languageEnglish
Pages (from-to)421-428
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Publication statusPublished - 1 Jan 2002


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