Resonance Tongues and Instability Pockets in the Quasi – Periodic Hill – Schrödinger Equation

  title={Resonance Tongues and Instability Pockets in the Quasi – Periodic Hill – Schr{\"o}dinger Equation},
  author={Henk W. Broer and Joaquim Puig and C. Sim{\'o}},
This paper concerns Hill’s equation with a (parametric) forcing that is real analytic and quasi-periodic with frequency vectorω ∈ R and a ‘frequency’(or ‘energy’) parameter a and a small parameter b. The 1-dimensional Schrödinger equation with quasi-periodic potential occurs as a particular case. In the parameter plane R2 = {a, b}, for small values of b we show the following. The resonance “tongues” with rotation number 1 2 〈k, ω〉,k ∈ Z haveC∞-boundary curves. Our arguments are based on… CONTINUE READING


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