Gherstega, N. N.; Popa, Mihail N.; Pricop, V. V. Generators of the algebras of invariants for differential system with homogeneous nonlinearities of odd degree. (English) Zbl 1271.34040 Bul. Acad. Ştiinţe Repub. Mold., Mat. 2012, No. 2(69), 43-58 (2012). Summary: 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 present a method of the construction of generators of the algebras of invariants for corresponding systems. MSC: 34C14 Symmetries, invariants of ordinary differential equations Keywords:polynomial differential system; common Hilbert series; generalized Hilbert series; algebras of invariants; algebras of comitants; Krull dimension × Cite Format Result Cite Review PDF Full Text: Link