Abstract
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 language | English |
---|---|
Pages (from-to) | 7613-7635 |
Journal | Journal of Physics A: Mathematical and General |
Volume | 33 |
Issue number | 42 |
DOIs | |
Publication status | Published - 27 Oct 2000 |