Direct product of unfurled swallowtails in the problem of going around an obstacle
type: Item
instance of: scholarly article
title: Direct product of unfurled swallowtails in the problem of going around an obstacle
zbMATH Open document ID: 0913.58004
DOI: 10.1007/BF02509615
author: O. M. Myasnichenko
publication date: 1997-11-04T00:00:00Z
review text: Lagrangian varieties arising in the problem of going around an obstacle bounded by a smooth hypersurface \(\Gamma\) in a smooth configuration manifold are studied. Let, for example, \(\Gamma\) be a smooth hypersurface in Euclidean space. Consider rays starting from a given point and touching \(\Gamma\). They define the variety \(l\) of geodesics on \(\Gamma\) starting from contact points of rays with \(\Gamma\). Let \(L\) be a variety of rays in the ambient space which break loose from the pencil of geodesics given by the variety \(l\). The author gives formal normal forms up to symplectomorphisms (diffeomorphisms) of a generic variety \(L\) in a neighbourhood of rays 2-tangent (3-tangent) to \(\Gamma\).
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 1053617
zbMATH Keywords: unfurled smallowtails
zbMATH Keywords: Lagrangian variety
zbMATH Keywords: problem of going around an obstacle
reviewed by: V. D. Sedykh
MaRDI profile type: Publication
cites work: Analytic classification of germs of conformal mappings \((C,O) \to (C,O)\) with identity linear part
cites work: Singular Lagrangian manifolds and their Lagrangian maps
cites work: Geodesics of the boundary in the obstacle problem and unfurled swallowtails
cites work: Equivalence of glancing hyper-surfaces
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1053617