Off-center Reflections: Caustics and Chaos

Details Off-center Reflections: Caustics and Chaos Off-center Reflections: Caustics and Chaos

1998-06-18

arxiv.org/abs/math/9806094v3

Mathematics

Dynamical Systems

26 pages, 20 figures, AMS-LaTeX, revised edition, no offset problem. To appear in Experimental Mathematics

Scientific paper

In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a generalization of standard perturbation of rotation. Some results of the caustics and dynamics of the family of maps are given. The method of symplectic topology is particularly exploited to study the caustics because of its potential in further development. The mode-locking behavior and width of resonance zone are also studied. Furthermore, there are interesting problems arised from experimental observations.

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