Stability and bifurcation of invariant tori from an equilibrium state of an essentially nonlinear second-order differential equation (Q845091)

From the abstract: ``Small periodic perturbations of the oscillator \(\ddot{x}+ x^2 \text{sgn} x =0\) are considered. Two problems are studied: the stability of the equilibrium state and the bifurcation to invariant \(2\)-tori from the equilibrium state. An algorithm for constructing a constant whose sign determines asymptotic stability or instability is suggested. Moreover, an equation whose every positive root corresponds to an invariant \(2\)-torus is constructed.''