Analytic conjugation between planar differential systems and potential systems

Abstract

In this article it is proved that an analytical planar vector field with a non-degenerate center at $(0,0)$ is analytically conjugate, in a neighborhood of $(0,0)$, to a Hamiltonian vector field of the form $y\frac{\partial }{\partial x}-V^{\prime }(x)\frac{\partial }{\partial y}$, where $V$ is an analytic function defined in a neighborhood of the origin such that $V(0)=V^{\prime }(0)=0$ and $V^{\prime \prime }(0)>0.$

08 pages

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• Analytic conjugation between planar differential systems and potential systems

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• Analytic conjugation between planar differential systems and potential systems