Geodesic
Generators of the algebras of invariants for differential system with homogeneous nonlinearities of odd degree
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 43-58.

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Common Hilbert series and generalized Hilbert series for the algebras of invariants and comitants of polynomial differential systems with homogeneous nonlinearities of the fifth degree are constructed, with their help the Krull dimensions of these algebras are obtained. The relations between Hilbert series of various algebras of invariants and comitants of polynomial differential systems with homogeneous nonlinearities of odd degree are given. With their help we give a method of the construction of generators of the algebras of invariants for corresponding systems. 
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N. N. Gherstega; M. N. Popa; V. V. Pricop. Generators of the algebras of invariants for differential system with homogeneous nonlinearities of odd degree. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 43-58. https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a3/

[1] Sibirsky K. S., Method of invariants in the qualitative theory of differential equations, RIO AN Moldavian SSR, Kishinev, 1968 (in Russian) | MR

[2] Sibirsky K. S., Algebraic invariants of differential equations and matrices, Shtiintsa, Kishinev, 1976 (in Russian)

[3] Sibirsky K. S., Introduction to the Algebraic Theory of Invariants of Differential Equations, Nonlinear Science: Theory and applications, Manchester University Press, Manchester, 1988 | MR | Zbl

[4] Vulpe N. I., Polynomial bases of comitants of differential systems and their application in qualitative theory, Shtiintsa, Kishinev, 1986 (in Russian) | MR | Zbl

[5] Boulars D., Dali D., Sur les bases des concomitants centro-affines des systemes differentiels, Cahiers mathematiques de l'Universite d'Oran, Oran, 1987

[6] Popa M. N., Applications of algebras to differential systems, Academy of Sciences of Moldova, 2001 (in Russian)

[7] Popa M. N., Algebraic methods for differential systems, Seria Matematică Aplicată şi Industrială, 15, Editura the Flower Power, Universitatea din Piteşti, 2004 (in Romanian) | MR | Zbl

[8] Springer T. A., Invariant theory, Springer-Verlag, Berlin–Heidelberg–New York, 1977 | MR | Zbl

[9] Chebanu V. M., “Minimal polynomial basis of comitants of cubic differential systems”, Differential equations, 21:3 (1985) (in Russian) | Zbl