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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1999, Volume 225, Pages 195–201 (Mi tm721)  

Polyhedral and Dihedral Caustics in the $\mathbb R^3$

A. Joetsa, M. I. Monastyrskiibac, R. Ribottaa

a Paris-Sud University 11
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
c Institut des Hautes Études Scientifiques
References:
Abstract: The role of the symmetries in the topology of sets of Lagrangian singularities is studied in a simple physical model: the envelope of the rays emanating from a convex wave front invariant under the action of discrete subgroups of $O(3)$. New point-singularities of integer index are found. They are located at the vertices of the polyhedron or of its dual. For the dihedral subgroups, we have found a remarkable property of stability of umbilics. These properties result from the interplay between the symmetries of the singularities and the topology of the wave front. An application to fine-particle magnetic systems is given.
Received in December 1998
Bibliographic databases:
UDC: 517+538.9
Language: English
Citation: A. Joets, M. I. Monastyrskii, R. Ribotta, “Polyhedral and Dihedral Caustics in the $\mathbb R^3$”, Solitons, geometry, and topology: on the crossroads, Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov, Trudy Mat. Inst. Steklova, 225, Nauka, MAIK «Nauka/Inteperiodika», M., 1999, 195–201; Proc. Steklov Inst. Math., 225 (1999), 183–189
Citation in format AMSBIB
\Bibitem{JoeMonRib99}
\by A.~Joets, M.~I.~Monastyrskii, R.~Ribotta
\paper Polyhedral and Dihedral Caustics in the~$\mathbb R^3$
\inbook Solitons, geometry, and topology: on the crossroads
\bookinfo Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov
\serial Trudy Mat. Inst. Steklova
\yr 1999
\vol 225
\pages 195--201
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm721}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1725941}
\zmath{https://zbmath.org/?q=an:0983.58019}
\transl
\jour Proc. Steklov Inst. Math.
\yr 1999
\vol 225
\pages 183--189
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    Òðóäû Ìàòåìàòè÷åñêîãî èíñòèòóòà èìåíè Â. À. Ñòåêëîâà Proceedings of the Steklov Institute of Mathematics
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