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On Classification of Planar Cubic Polynomials

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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

CLC Number:

O192

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

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