维格纳苛集和中心对称集的艺术方面

arXiv - MATH - General Mathematics Pub Date : 2024-08-14 DOI:arxiv-2409.04443

Iza Danielewska, Dawid Poławski, Dominika Sterczewska, Michał Zwierzyński

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引用次数: 0

摘要

维格纳苛集和闭合光滑平面曲线的中心对称集是已知的奇异集，它们一般只允许尖点奇异性。这些对象在半经典量子物理学、混沌理论、奇异性理论和凸几何学中的应用，自上世纪 70 年代开始研究至今。这些集合可以看作是特殊线族的包络，因此它们具有许多几何艺术价值。

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Artistic Aspects of the Wigner Caustic and the Centre Symmetry Set

The Wigner caustic and the Centre Symmetry Set of a closed smooth planar curve are known singular sets which generically admit only cusp singularities. Applications of these objects in semi-classical quantum physics, in chaos theory, in singularity theory, in convex geometry, have been studied since the 1970s until today. These sets can be viewed as envelopes of special families of lines and thanks to that they have many geometric artistic values.

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arXiv - MATH - General Mathematics

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