N Sadovskaia and R Ramírez 2004 J. Phys. A: Math. Gen. 37 3847 doi:10.1088/0305-4470/37/12/009
N Sadovskaia1 and R Ramírez2
Show affiliationsWe construct a polynomial differential system that admits a given set of invariant algebraic curves. For such a system we solve the Darboux problem (the existence of the Darboux first integral), the Poincaré problem (the existence of an upper bound for the degree of invariant algebraic curve) and study Hilbert's 16th problem for algebraic limit cycles (the existence of an upper bound for the number of algebraic limit cycles).
Issue 12 (26 March 2004)
Received 8 September 2003, in final form 22 December 2003
Published 10 March 2004
N Sadovskaia and R Ramírez 2004 J. Phys. A: Math. Gen. 37 3847
A A Risbud 2004 J. Phys. A: Math. Gen. 37 6837
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