## Periodic Solutions and Chaotic Dynamics in Forced Impact Oscillators

- Alfonso Ruiz-Herrera, Pedro J. Torres
- SIAM J. Applied Dynamical Systems
- 2013

1 Excerpt

- Published 2000

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

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