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Center conditions for polynomial Liénard equation. (English) Zbl 1199.34163
Summary: Necessary and sufficient conditions are studied for the coefficients of the polynomials $$f (x)$$ and $$g (x)$$ such that the Liénard equation $$\ddot{x}+f (x)\dot{x}+g (x)=0$$ has non-degenerate centers. An algorithm to calculate the center conditions is presented.
MSC:
 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations