Periodic perturbations of a nonlinear oscillator

We study small time-periodic perturbations of an oscillator with a power-law odd restoring force with exponent exceeding unity. We study two problems, one on the stability of the equilibrium and the other on the bifurcation of an invariant two-dimensional torus from the equilibrium. We construct a focal quantity and a bifurcation equation that find the character of stability and branching of the equilibrium.