Communications in Mathematical Physics

, Volume 143, Issue 1, pp 43–83

Quasiperiodic motions in superquadratic time-periodic potentials


  • Mark Levi
    • Department of Mathematical SciencesReusselaer Polytechnic Institute

DOI: 10.1007/BF02100285

Cite this article as:
Levi, M. Commun.Math. Phys. (1991) 143: 43. doi:10.1007/BF02100285


It is shown that for a large class of potentials on the line with superquadratic growth at infinity and with the additional time-periodic dependence all possible motions under the influence of such potentials are bounded for all time and that most (in a precise sense) motions are in fact quasiperiodic. The class of potentials includes, as very particular examples, the exponential, polynomial and much more. This extends earlier results and gives an answer to a problem posed by Littlewood in the mid 1960's. Along the way machinery is developed for estimating the action-angle transformation directly in terms of the potential and also some apparently new identities involving singular integrals are derived.

Copyright information

© Springer-Verlag 1991