Integrability and linearizability of the Lotka-Volterra system with a saddle point with rational hyperbolicity ratio (Q701066)

This paper deals with normalizability, integrability and linearizability properties of a Lotka-Volterra system in a neighborhood of a singular point with eigenvalues 1 and \(-\lambda\). The results are obtained by generalizing and extending two methods already known: the power expansion of the first integral or of the linearizing transformation and the transformation of a saddle into a node. Using these methods, the authors derive sufficient conditions for \(\lambda\in\mathbb R^+\) or \(\lambda\in\mathbb Q\) to obtain all integrable and linearizable systems for \(\lambda=p/2\) and \(2/p\) with \(p\in\mathbb N^+\).