The Wigner caustic on shell and singularities of odd functions

Autor(es)

Domitrz, Wojciech ^[1] ; Manoel, Miriam ^[2] ; Rios, Pedro de M. ^[2]

Afiliação do(s) autor(es)

^[1] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00662 Warsaw - Poland

^[2] Univ Sao Paulo, ICMC, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF GEOMETRY AND PHYSICS; v. 71, p. 58-72, SEP 2013.
• Citações Web of Science: 6

Resumo

We study the Wigner caustic on shell of a Lagrangian submanifold L of affine symplectic space. We present the physical motivation for studying singularities of the Wigner caustic on shell and present its mathematical definition in terms of a generating family. Because such a generating family is an odd deformation of an odd function, we study simple singularities in the category of odd functions and their odd versal deformations, applying these results to classify the singularities of the Wigner caustic on shell, interpreting these singularities in terms of the local geometry of L. (C) 2013 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 10/15179-8 - Geometria simplética aplicada a física matemática
• Beneficiário: Pedro Paulo de Magalhaes Rios
• Modalidade de apoio: Auxílio à Pesquisa - Regular