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<p>In this paper, through algebraic invariant theory, we reduce many-dimensional polynomial differential systems to the normal canonical forms with coefficients expressed as rational functions of the covariants of these systems. Consequently, we show that these constructed normal forms lead to the determination of rational bases of invariants, covariants and affine covariants for these systems. In addition, algebraic conditions are given for the problem of the centro-affine equivalence between polynomial differential systems in terms of the invariants of these constructed rational bases.</p>

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Rational Bases of Covariants of Many-Dimensional Polynomial Differential Systems

  • 期刊论文

  • 发表日期：

    2025年3月20日

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  • Abderrahmane Turqui,
  • Anis Hezzam

摘要

In this paper, through algebraic invariant theory, we reduce many-dimensional polynomial differential systems to the normal canonical forms with coefficients expressed as rational functions of the covariants of these systems. Consequently, we show that these constructed normal forms lead to the determination of rational bases of invariants, covariants and affine covariants for these systems. In addition, algebraic conditions are given for the problem of the centro-affine equivalence between polynomial differential systems in terms of the invariants of these constructed rational bases.