平面三次多项式的分类

数学物理学报 ›› 2025, Vol. 45 ›› Issue (2): 554-566.

平面三次多项式的分类

李林¹,刘玲伶²,余志恒^3,^*()

¹嘉兴大学数学系浙江嘉兴 314001
²西南石油大学理学院成都 610500
³西南交通大学数学学院成都 611756

收稿日期:2023-10-31 修回日期:2024-10-15 出版日期:2025-04-26 发布日期:2025-04-09
通讯作者: 余志恒 E-mail:yuzhiheng9@163.com.
基金资助:
国家自然科学基金(11871041);国家自然科学基金(12171337);四川省自然科学基金(2022NSFSC1834);四川省自然科学基金(2023NSFSC0064);中央高校基本科研业务费(2682021ZTPY041);四川省中央引导地方科技发展专项(2024ZYD0059)

On Classification of Planar Cubic Polynomials

Li Lin¹,Liu Lingling²,Yu Zhiheng^3,^*()

¹Faculty of Mathematics, Jiaxing University, Zhejiang Jiaxing 314001
²School of Sciences, Southwest Petroleum University, Chengdu 610500
³School of Mathematics, Southwest Jiaotong University, Chengdu 611756

Received:2023-10-31 Revised:2024-10-15 Online:2025-04-26 Published:2025-04-09
Contact: Zhiheng Yu E-mail:yuzhiheng9@163.com.
Supported by:
NSFC(11871041);NSFC(12171337);National Science Foundation of Sichuan Province(2022NSFSC1834);National Science Foundation of Sichuan Province(2023NSFSC0064);Fundamental Research Funds for the Central Universities(2682021ZTPY041);Central Government Guided Local Science and Technology Development Projects(2024ZYD0059)

摘要/Abstract

摘要：

该文将讨论平面多项式的正规形理论. 作者利用多项式代数理论求出相应变量的最小不可约分解, 并通过全局共轭得到一类平面三次多项式的光滑分类. 作者的定理还应用于讨论平面迭代根与嵌入流问题.

关键词: 平面三次多项式, 共轭, 光滑正规形, 最小不可约分解, 迭代根

Abstract:

In this paper, we consider cubic polynomial normal forms on $\mathbb{R}^2$. By employing the theory of polynomial algebra to find the minimal irreducible decomposition of the corresponding varieties, we obtain smooth classifications of a kind of planar cubic polynomials via global conjugations. Our results are also applied to study the problems of iterative roots and embedding flows on $\mathbb{R}^2$.

Key words: planar cubic polynomial, conjugacy, smooth normal form, minimal irreducible decomposition, iterative root

中图分类号:

O192

李林,刘玲伶,余志恒. 平面三次多项式的分类[J]. 数学物理学报, 2025, 45(2): 554-566.

Li Lin,Liu Lingling,Yu Zhiheng. On Classification of Planar Cubic Polynomials[J]. Acta mathematica scientia,Series A, 2025, 45(2): 554-566.

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