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IMCS/Publications/BASM/Issues/BASM n.2 (69), 2012/

Generators of the algebras of invariants for differential system with homogeneous nonlinearities of odd degree

Authors: N. N. Gherstega, Popa Mihail, Pricop Victor
Keywords: Diferential system, common Hilbert series, generalized Hilbert series, algebras of invariants and comitants, Krull dimension.

Abstract

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.

Institute of Mathematics and Computer Science
Academy of Sciences of Moldova
5, Academiei str. Chişinău, MD-2028, Moldova
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