Corrections and complements to “Liouvillian integration of the Lotka-Volterra system”
Copyright policy )Corrections and complements to “Liouvillian integration of the Lotka-Volterra system”
In the original paper [the author, Qual. Theory Dyn. Syst. 2, No. 2, 307--358 (2002; Zbl 1084.34001)] the author described all possible values of the non-zero parameters \(A\), \(B\), and \(C\) for which the vector field \( x(Cy+z)\partial/\partial x + y(Az+x)\partial/\partial y + z(Bx+y)\partial/\partial z \) admits a homogeneous Liouvillian first integral of degree zero. He also treated degenerate cases in which \(ABC = 0\). Omissions and errors that were discovered in these additional cases are corrected in this paper, using ideas and techniques of the original article.
- École Polytechnique France
- Paris-East Créteil University France
Explicit solutions, first integrals of ordinary differential equations, Dynamics induced by flows and semiflows, Liouvillian first integral, Lotka-Volterra
Explicit solutions, first integrals of ordinary differential equations, Dynamics induced by flows and semiflows, Liouvillian first integral, Lotka-Volterra
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