Invariant algebraic surfaces of the Rikitake system

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

38 Citations (Scopus)


In this paper we use the method of characteristic curves for solving linear partial differential equations to study the invariant algebraic surfaces of the Rikitake system ẋ = -μx + y(z + β) ẏ = -μy + x (z - β) ż = α - xy. Our main results are the following. First, we show that the cofactor of any invariant algebraic surface is of the form rz + c, where r is an integer. Second, we characterize all invariant algebraic surfaces. Moreover, as a corollary we characterize all values of the parameters for which the Rikitake system has a rational or algebraic first integral.
Original languageEnglish
Pages (from-to)7613-7635
JournalJournal of Physics A: Mathematical and General
Issue number42
Publication statusPublished - 27 Oct 2000


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