Abstract
This paper is concerned with limit cycles which bifurcate from periodic orbits of the cubic isochronous center. It is proved that in this situation, the cyclicity of the period annulus under cubic perturbations is equal to four. Moreover, for each k = 0,1, . . .,4, there are perturbations that give rise to exactly k limit cycles bifurcating from the period annulus.
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Research partially supported by the NSF of China (No.10871214), the Ph.D. Programs Foundation of Ministry of Education of China (No. 20100171110040) and Program for New Century Excellent Talents in University.
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Wu, K., Zhao, Y. The cyclicity of the period annulus of the cubic isochronous center. Annali di Matematica 191, 459–467 (2012). https://doi.org/10.1007/s10231-011-0190-5
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DOI: https://doi.org/10.1007/s10231-011-0190-5