Center and Isochronous Center at Infinity in a Class of Planar Differential Systems
نویسندگان
چکیده
In this paper, the conditions of center and isochronous center at the infinity for a class of planar differential systems are studied. By a transformation, we first transform the infinity (the equator) of the systems into the origin. Then sufficient and necessary conditions for the infinity (the equator) of the systems being a center are obtained. A Construction Theorem of periodic constants is presented, which plays an important role in simplifying periodic constants. A complete classification of the sufficient and necessary conditions is given for the infinity of the systems being an isochronous center. All the computations for the quantities at infinity and periodic constants are performed using computer algebraic system – Mathematics 4.2, and the technique employed in this paper is different from others used in the literature.
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