Abstract
In this article, we investigate the necessary and sufficient conditions for the existence of isochronous centers at infinity into a class of rational differential system. Firstly, we give a transformation taking infinity to the origin, therefore we can study the properties of infinity with methods of the origin. By means of computing singular point quantities and period constants at the origin for the transformed system, we find necessary conditions for such isochronous centers. Finally, we prove these conditions are also sufficient. What’s worth mentioning is that for some systems, we prove the sufficiency of isochronous center conditions with several methods.
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This research is partially supported by the National Nature Science Foundation of China (10771196).
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Wu, Y., Huang, W. & Dai, H. Isochronicity at Infinity into a Class of Rational Differential System. Qual. Theory Dyn. Syst. 10, 123–138 (2011). https://doi.org/10.1007/s12346-011-0041-1
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DOI: https://doi.org/10.1007/s12346-011-0041-1