多项式向量场的等时性与交换性
Isochronicity and Commutation of Polynomial Vector Fields
摘要：
研究了多项式向量场中心的等时性与多项式交换系统存在性之间的联系。我们证明了一个不与任何多项式系统交换的4次等值线系统。证明了在Newton多项式系统中，只有Lienard和Abel系统可以与横截多项式域交换。我们给出了Abel多项式系统的中心化子的一个完整的和建设性的描述。我们给出了新的例子的isoorthoscopic系统。
英文摘要：
We study a connection between the isochronicity of a center of a polynomial vector field and the existence of a polynomial commuting system. We demonstrate an isochronous system of degree 4 which does not commute with any polynomial system. We prove that among the Newton polynomial systems only the Lienard and Abel systems may commute with transversal polynomial fields. We give a full and constructive description of centralizers of the Abel polynomial systems. We give new examples of isochronous systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
