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