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arXiv · 2404.02036

Analytic conjugation between planar differential systems and potential systems

F. J. S. Nascimento
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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 $y\frac{\partial}{\partial x}-V'(x)\frac{\partial}{\partial y}$, where $V$ is an analytic function defined in a neighborhood of the origin such that $V(0)=V'(0)=0$ and $V''(0)>0.$

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F. J. S. Nascimento. 2024-04-02. Analytic conjugation between planar differential systems and potential systems. https://doi.org/10.21167/cqdv24e24015

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