Time-Dependent Circular Billiard

J. E. Howard

Mathematical Problems in Engineering, 2009, vol. 2009, 1-10

Abstract:

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:531024

DOI: 10.1155/2009/531024

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