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arXiv · 1906.07425

On the transformations linearizing isochronous centers of Hamiltonian systems

Guangfeng Dong·Yuyi Zhang
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Abstract

In this paper we study the transformations linearizing isochronous centers of planar Hamiltonian differential systems with polynomial Hamiltonian functions $H(x,y)$ having only isolated singularities. Assuming the origin is an isochronous center lying on the level curve $L_0$ defined by $H(x,y)=0$, we prove that, there exists a canonical linearizing transformation analytic on a simply-connected open set $\Omega$ with closure $\overline{\Omega}=\mathbb{R}^2$, if and only if, $L_0$ consists of only isolated points; furthermore, if the origin is the unique center, then the condition that $L_0$ consists of only isolated points implies that the corresponding canonical linearizing transformation can be analytically defined on the whole plane.

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Guangfeng Dong, Yuyi Zhang. 2019-06-18. On the transformations linearizing isochronous centers of Hamiltonian systems. https://arxiv.org/abs/1906.07425

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