Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi–Ulam problem

Abstract

In this paper the monotonic twist theorem is extended to the quasiperiodic case and applied to establish regularity of motion in a system of a particle bouncing elastically between two quasiperiodically moving walls. It is shown that the velocity of the particle is uniformly bounded in time if the frequencies satisfy a Diophantine inequality. This answers a question recently asked in Levi and Zehnder (1995 SIAM J. Math. Anal. 26 1233–56). AMS classification scheme numbers: 37J40, 70H08

Cite this paper

@inproceedings{Zharnitsky2000InvariantCT, title={Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi–Ulam problem}, author={Vadim Zharnitsky}, year={2000} }