Rational Bases of Covariants of Many-Dimensional Polynomial Differential Systems

• Abderrahmane Turqui ^[1] ; Anis Hezzam ^[2]
  1. [1] University Center Aflou
  2. [2] University of Sciences and Technology Houari Boumediene
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.

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