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TitleMinimum number of ideal generators for a linear center perturbed by homogeneous polynomials
Author(s) Jaume Giné, Josep Mallol
TypeArticle in Journal
AbstractUsing the algorithm presented in [J. Giné, X. Santallusia, On the Poincaré–Liapunov constants and the Poincaré series, Appl. Math. (Warsaw) 28 (1) (2001) 17–30] the Poincaré–Liapunov constants are calculated for polynomial systems of the form x ̇ = − y + P n ( x , y ) , y ̇ = x + Q n ( x , y ) , where P n and Q n are homogeneous polynomials of degree n . The objective of this work is to calculate the minimum number of ideal generators i.e., the number of functionally independent Poincaré–Liapunov constants, through the study of the highest fine focus order for n = 4 and n = 5 and compare it with the results that give the conjecture presented in [J. Giné, On the number of algebraically independent Poincaré–Liapunov constants, Appl. Math. Comput. 188 (2) (2007) 1870–1877]. Moreover, the computational problems which appear in the computation of the Poincaré–Liapunov constants and the determination of the number of functionally independent ones are also discussed.
KeywordsPoincaré–Liapunov constants, Fine focus order, Center problem, Groebner basis
URL http://www.sciencedirect.com/science/article/pii/S0362546X08005373
JournalNonlinear Analysis: Theory, Methods & Applications
Pagese132 - e137
Translation No
Refereed No