Single-well periodic orbit range for the weakly perturbed double-well oscillator
= Single-well periodic orbit range for the weakly perturbed double-well oscillator
For the periodic energy levels $-1/4<H_0<0$ enclosing one well, the energy-balance value of $\alpha$ ranges from one at the center to $5/4$ at the homoclinic loop. Thus for small positive $\varepsilon$, one expects one symmetric pair of single-well periodic orbits when $1<\alpha<5/4$.