具有多项式换向器的六度均匀等时中心系统的全局相位特征

Pub Date : 2024-06-05 DOI:10.1007/s10255-024-1081-z

Li-na Guo, Ai-yong Chen, Shuai-feng Zhao

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摘要

本文研究了具有多项式换向器的六度均匀等时中心系统的全局相位肖像。此类系统的形式为（dot x = - y + xf(x,\,y),\,\dot y = x + yf(x,\,y)\), 其中f(x, y) = a1x + a2xy + a3xy2 + a4xy3 + a5xy4 = xσ(y)、和 1 + a1y + a2y2 + a3y3 + a4y4 + a5y5 的任意零点，（y = （bar y\ ）是一条不变直线。最后，所有的全局相位肖像都画在波恩卡莱圆盘上。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator

This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial commutator. Such systems have the form \(\dot x = - y + xf(x,\,y),\,\,\dot y = x + yf(x,\,y)\), where f(x, y) = a₁x + a₂xy + a₃xy² + a₄xy³ + a₅xy⁴ = xσ(y), and any zero of 1 + a₁y + a₂y² + a₃y³ + a₄y⁴ + a₅y⁵, \(y = \bar y\) is an invariant straight line. At last, all global phase portraits are drawn on the Poincaré disk.

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