The equivalence between singular point quantities and Liapunov constants on center manifold

The algorithm of singular point quantities for an equilibrium of three-dimensional dynamics system is studied. The explicit algebraic equivalent relation between singular point quantities and Liapunov constants on center manifold is rigorously proved. As an example, the calculation of singular point quantities of the Lü system is applied to illustrate the advantage in investigating Hopf bifurcation of three-dimensional system.MR (2000) Subject Classification: 34C23, 34C28, 37Gxx.

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