| Abstract: |
| In this talk we investigate center-related problems for generalized Kukles systems. We derive sufficient and necessary conditions for the origin of such systems with $\mathbb{Z}_2$-symmetry or weak $\mathbb{Z}_2$-symmetry to be a center. Moreover, we provide examples to illustrate the center conditions using our theoretical results and give a negative answer to a conjecture proposed in the literature. Moreover, we investigate the problem of integrability for general generalized Kukles systems when they admit a center. |
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