Singular points of the Wigner caustic and affine equidistants of planar curves

DOI10.1007/s00574-019-00141-4zbMath1440.53003arXiv1810.04618OpenAlexW2897603741WikidataQ128101948 ScholiaQ128101948MaRDI QIDQ2174203

Wojciech Domitrz, Michał Zwierzyński

Publication date: 21 April 2020

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.04618

zbMATH Keywords

singularitiesaffine equidistantsWigner causticplanar curvessemiclassical dynamics

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Curves in Euclidean and related spaces (53A04) Affine differential geometry (53A15) Critical points of functions and mappings on manifolds (58K05)

Related Items (8)

Offsets and front tire tracks to projective hedgehogs ⋮ The Gauss-Bonnet theorem for coherent tangent bundles over surfaces with boundary and its applications ⋮ Isoperimetric equalities for rosettes ⋮ On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential ⋮ The geometry of the secant caustic of a planar curve ⋮ Singular improper affine spheres from a given Lagrangian submanifold ⋮ The geometry of the Wigner caustic and a decomposition of a curve into parallel arcs ⋮ Equi-affine plane curves with singular points

Cites Work

• The improved isoperimetric inequality and the Wigner caustic of planar ovals
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• Bifurcations of the center of symmetry
• The geometry of the secant caustic of a planar curve
• Singularities of affine equidistants: extrinsic geometry of surfaces in 4-space
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• The middle hedgehog of a planar convex body
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