Piecewise Isometries — An Emerging Area of Dynamical Systems
Piecewise Isometries — An Emerging Area of Dynamical Systems
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分段等距——动态系统的新兴领域
DOI：
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发表时间：
2003
期刊：
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通讯作者：
A. Goetz
中科院分区：
文献类型：
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作者：
A. Goetz
我们提出了几个例子，分段等距系统，产生复杂的结构，他们的编码分区。我们还列出和评论目前在该地区的开放问题，涉及到分形结构的细胞。分段等距是区间交换和区间平移的二维和高维推广。分段等距的动力系统的兴趣是部分催化的潜在应用和简单的几何结构产生丰富的现象和惊人的分形图形的事实。分段等距系统出现在对偶台球、哈密顿系统和数字滤波器中。
We present several examples of piecewise isometric systems that give rise to complex structures of their coding partitions. We also list and comment on current open questions in the area that pertain to fractal-like structure of cells. Piecewise isometries are two and higher dimensional generalizations of interval exchanges and interval translations. The interest in the dynamical systems of piecewise isometries is partially catalyzed by potential applications and the fact that simple geometric constructions give rise to rich phenomena and amazing fractal graphics. Piecewise isometric systems appear in dual billiards, Hamiltonian systems, and digital filters.