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Volume 7, Number 4, 2017, Pages 1463-1477                                                                DOI:10.11948/2017089
Limit cycle bifurcation for a nilpotent system in $Z_3$-equivariant vector field
Chaoxiong Du,Qinlong Wang,Yirong Liu,Qi Zhang
Keywords:Third-order nilpotent critical point, $Z_3$-equivariant, limit cycle bifurcation, Quasi-Lyapunov constant.
Abstract:
      Our work is concerned with the problem on limit cycle bifurcation for a class of $Z_3$-equivariant Lyapunov system of five degrees with three third-order nilpotent critical points which lie in a $Z_3$-equivariant vector field. With the help of computer algebra system-MATHEMATICA, the first 5 quasi-Lyapunov constants are deduced. The fact of existing 12 small amplitude limit cycles created from the three third-order nilpotent critical points is also proved. Our proof is algebraic and symbolic, obtained result is new and interesting in terms of nilpotent critical points' Hilbert number in equivariant vector field.
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