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Centers and Isochronous Centers of Liénard Systems
Differential Equations, 2019Holomorphic Liénard systems are studied. The authors give necessary and sufficient conditions for the existence of a center and an isochronous center which are obtained without calculating the focus quantities and the isochronicity constants.
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Isochronous Centers in Planar Polynomial Systems
SIAM Journal on Mathematical Analysis, 1997The authors consider the following planar system \[ \dot x = P(x,y),\quad \dot y = Q(x,y),\qquad (x,y)\in \mathbb{R}^2 \tag{1} \] where \(P\) and \(Q\) are polynomials in \(x\) and \(y\). Let the system (1) have a center, and let \(T\) be a period-function, i.e.
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