A method based on transcendental invariant curves with polynomial or rational cofactors is used to prove integrability for selected nonlinear oscillators and Painlevé-Gambier systems by solving linear algebraic and ODE problems.
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Integrability of oscillators and transcendental invariant curves
A method based on transcendental invariant curves with polynomial or rational cofactors is used to prove integrability for selected nonlinear oscillators and Painlevé-Gambier systems by solving linear algebraic and ODE problems.