Normal Form for Systems with Linear Part N3(n)

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References

[1] R. Cushman, J. A. Sanders and N. White, “Normal Form for the (2;n)-Nilpotent Vector Field Using Invariant Theory,” Physica D: Nonlinear Phenomena, Vol. 30, No. 3, 1988, pp. 399-412. doi:10.1016/0167-2789(88)90028-0

[2] D. M. Malonza “Normal Forms for Coupled Takens-Bogdanov Systems,” Journal of Nonlinear Mathematical Physics, Vol. 11, No. 3, 2004, pp. 376-398.
doi:10.2991/jnmp.2004.11.3.8

[3] W. W. Adams and P. Loustaunau, “An Introduction to Gr?bner Bases,” American Mathematical Society, Providence, 1994.

[4] J. Murdock and J. A. Sanders, “A New Transvectant Algorithm for Nilpotent Normal Forms,” Journal of Differential Equations, Vol. 238, No. 1, 2007, pp. 234-256.
doi:10.1016/j.jde.2007.03.016

[5] N. Sri NAmachchivaya, M. M. Doyle, W. F. Langford and N. W. Evans, “Normal Form for Generalized Hopf Bifurcation with Non-Semisimple 1:1 Resonance,” Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 45, No. 2, 1994, pp. 312-335.
doi:10.1007/BF00943508

[6] G. Gachigua and D. Malonza, “Stanley Decomposition of Coupled N333 System,” Proceedings of the 1st Kenyatta University International Mathematics Conference, Nairobi, 6-10 June 2011, pp. 39-52.