Details:
Title  Minimum number of ideal generators for a linear center perturbed by homogeneous polynomials  Author(s)  Jaume Giné, Josep Mallol  Type  Article in Journal  Abstract  Using 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.  Keywords  Poincaré–Liapunov constants, Fine focus order, Center problem, Groebner basis  ISSN  0362546X 
URL 
http://www.sciencedirect.com/science/article/pii/S0362546X08005373 
Language  English  Journal  Nonlinear Analysis: Theory, Methods & Applications  Volume  71  Number  12  Pages  e132  e137  Year  2009  Edition  0  Translation 
No  Refereed 
No 
