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Evaluating cyclicity of cubic systems with algorithms of computational algebra

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  • We describe an algorithmic approach to studying limit cycle bifurcations in a neighborhood of an elementary center or focus of a polynomial system. Using it we obtain an upper bound for cyclicity of a family of cubic systems. Then using a theorem by Christopher [3] we study bifurcation of limit cycles from each component of the center variety. We obtain also the sharp bound for the cyclicity of a generic time-reversible cubic system.
    Mathematics Subject Classification: Primary: 34C07; Secondary: 34C23.


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