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arXiv · 2311.10020

On the non-existence of isochronous centers in planar discontinuous differential systems

Ali Bakhshalizadeh·Changjian Liu·Alex C. Rezende
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Abstract

The determination of whether a center is isochronous or not is a well-known problem in the qualitative theory of planar systems. In this paper, we explore planar piecewise discontinuous differential systems characterized by a straight switching line $y=0$ and $x=0$, respectively. Our investigation reveals that such systems do not possess an isochronous center at the origin.

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Ali Bakhshalizadeh, Changjian Liu, Alex C. Rezende. 2023-11-16. On the non-existence of isochronous centers in planar discontinuous differential systems. https://arxiv.org/abs/2311.10020

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