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Conflict sets, orthotomics, pedals and billiards as canonical relations

Published online by Cambridge University Press:  28 September 2006

M. van MANEN
M. van MANEN
Affiliation:
Department of Mathematics, Hokkaido University Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan.
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Abstract

Conflict sets are loci of intersecting wave fronts emanating from $l$ different manifolds. We show that for generic manifolds their conflict sets are projections of smooth conic Lagrangian manifolds. Thus conflict sets locally admit the structure of wave fronts. Simple stable singularities for this problem in $\mathbb{R}^n$ occur when $0\leq n-l \leq 4$. Relations with centre sets, billiards, pedals and orthotomics are also discussed. Throughout canonical relations are used as an essential tool to carry out these geometrical constructions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 141 , Issue 2 , September 2006 , pp. 339 - 353
Copyright
2006 Cambridge Philosophical Society

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