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

@inproceedings{Broer2003ResonanceTA,
  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}},
  year={2003}
}
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

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 27 references

A reversible bifurcation analysis of the inverted pendulum

H. W. Broer, I. Hoveijn, M. van Noort
Bifurcations in Hamiltonian Systems , computing singularities by Gröbner bases . Lecture Notes in Math . 1806 • 2003

Equivariant singularity theory with distinguished parameters : Two case - studies of resonant Hamiltonian systems

H. W. Broer, G. A. Lunter, G. Vegter
Physica D • 2003

Localization for a class of one - dimensional quasi - periodic Schrödinger operators

J. Fröhlich, T. Spencer, P. Wittwer
Commun . Math . Phys . • 2002

Normal forms of twist maps in a resonant annulus

A. Olvera, C. Simó
1998

Resonance tongues in Hill ’ s equations : A geometric approach

H. W. Broer, C. Simó
J . Diff . Eqs . • 1998

Geometrical aspects of stability theory for Hill ’ s equations

H. W. Broer, M. Levi
Physica D • 1997

Similar Papers

Loading similar papers…