Off - Center Reflections : Caustics and Chaos Thomas Kwok - Keung Au
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چکیده
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.
منابع مشابه
Off-Center Reflections: Caustics and Chaos
We study the properties of a particular one-parameter family of circle maps called offcenter reflections defined in §2. This map, in its 2-dimensional version, is first introduced in an open problem by S. T. Yau, [Y, problem 21], who suggests a cross study of the dynamics and geometry. In this article, we attempt to explore the possible link between the dynamics of this family of circle maps an...
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تاریخ انتشار 1998