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Improved K-K algorithm for computing Lyapunov values. (English) Zbl 0811.34030
The classical center-focus problem in the plane is investigated. A modified algorithm is given for the calculation of the Lyapunov values (i.e. coefficients of the radial terms in the normal form). In case of 3 presented examples some of these values are calculated by computer algebra. The new method needs less computer time and memory than the one proposed by V. Kertész and R. E. Kooij [Nonlinear Anal., Theory Methods Appl. 17, No. 3, 267-283 (1991; Zbl 0735.34031)]. The results can be used among others in Hopf-type bifurcation problems and in construction of planar systems with a large number of periodic orbits.
MSC:
34C23 Bifurcation theory for ordinary differential equations
68W30 Symbolic computation and algebraic computation
37G99 Local and nonlocal bifurcation theory for dynamical systems
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