Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 531024, 10 pages
Research Article

Time-Dependent Circular Billiard

Center for Integrated Plasma Studies, Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, CO 80309, USA

Received 6 May 2009; Revised 8 July 2009; Accepted 15 July 2009

Academic Editor: Edson Denis Leonel

Copyright © 2009 J. E. Howard. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate a time-dependent circular billiard with a two-frequency driving function and derive a new simplified form for the map, which is a symplectic nontwist map. Stability boundaries and reconnection thresholds are derived for fixed points and period-two vortex pairs. An island interspersal condition is derived such that neighboring island chains of the first frequency are exactly separated by those of the second. The results show a strong enhancement of the KAM barrier to chaotic diffusion with increasing second frequency content and overall amplitude.