Beltran, J. V.; Monterde, J. A reflecting sundial with cusps of the caustics on a straight line segment. (English) Zbl 07971574 J. Geom. 116, No. 1, Paper No. 2, 14 p. (2025). MSC: 53A04 58K05 × Cite Format Result Cite Review PDF Full Text: DOI
Dias, L. R. G.; Farnik, M.; Jelonek, Z. Generic symmetry defect set of an algebraic curve. (English) Zbl 1548.14035 Proc. Am. Math. Soc. 152, No. 7, 2739-2749 (2024). Reviewer: Tien-Son Pham (Đà Lạt) MSC: 14D06 14Q20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Domitrz, Wojciech; Zwierzyński, Michał The geometry of the Wigner caustic and a decomposition of a curve into parallel arcs. (English) Zbl 1484.53014 Anal. Math. Phys. 12, No. 1, Paper No. 7, 35 p. (2022). Reviewer: Andreas Arvanitoyeorgos (Patras) MSC: 53A04 53A15 58K05 81Q20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Domitrz, W.; Romero Fuster, M. C.; Zwierzyński, M. The geometry of the secant caustic of a planar curve. (English) Zbl 1482.53005 Differ. Geom. Appl. 78, Article ID 101797, 22 p. (2021). Reviewer: Laurian Ioan Piscoran (Baia Mare) MSC: 53A04 53A15 58K05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ishikawa, G. Normal and tangent maps to frontals. (English. Russian original) Zbl 1480.53002 J. Math. Sci., New York 255, No. 5, 664-677 (2021); translation from Probl. Mat. Anal. 109, 119-130 (2021). Reviewer: Dorin Andrica (Riyadh) MSC: 53A07 58K05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Batista, Erica Boizan; Han, Huhe; Nishimura, Takashi Simultaneous smoothness and simultaneous stability of a \(C^\infty\) strictly convex integrand and its dual. (English) Zbl 1444.58013 Kodai Math. J. 43, No. 2, 221-242 (2020). MSC: 58K05 52A05 58K30 52A55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Domitrz, Wojciech; Zwierzyński, Michał Singular points of the Wigner caustic and affine equidistants of planar curves. (English) Zbl 1440.53003 Bull. Braz. Math. Soc. (N.S.) 51, No. 1, 11-26 (2020). Reviewer: Ergin Bayram (Samsun) MSC: 53A04 53A15 58K05 81Q20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tsar’kov, Igor’ G. Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function. (English. Russian original) Zbl 1429.41034 Izv. Math. 83, No. 6, 1234-1258 (2019); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 6, 167-194 (2019). MSC: 41A65 54C60 78A05 × Cite Format Result Cite Review PDF Full Text: DOI
Domitrz, W.; Janeczko, S.; de M. Rios, P.; Ruas, M. A. S. Singularities of affine equidistants: extrinsic geometry of surfaces in 4-space. (English) Zbl 1392.53012 Bull. Braz. Math. Soc. (N.S.) 47, No. 4, 1155-1179 (2016). MSC: 53A07 53A05 58K05 58K25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Josse, Alfrederic; Pène, Françoise On the class of caustics by reflection of planar curves. (English) Zbl 1330.14055 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 14, No. 3, 881-906 (2015). Reviewer: Hans-Peter Schröcker (Innsbruck) MSC: 14H50 14E05 14N05 14N10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alharbi, Fawaz Quasi cusp singularities. (English) Zbl 1308.58024 J. Singul. 12, 1-18 (2015). MSC: 58K05 58K40 53A15 × Cite Format Result Cite Review PDF Full Text: DOI
Janeczko, S.; Jelonek, Z.; Ruas, M. A. S. Symmetry defect of algebraic varieties. (English) Zbl 1343.14050 Asian J. Math. 18, No. 3, 525-544 (2014). Reviewer: Carlos D’Andrea (Barcelona) MSC: 14R10 13P10 14D06 14Q20 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Reeve, Graham M.; Zakalyukin, Vladimir M. Propagations from a space curve in three space with indicatrix a surface. (English) Zbl 1292.58026 J. Singul. 6, 131-145 (2012). MSC: 58K05 58K40 53A15 × Cite Format Result Cite Review PDF Full Text: DOI Link
Saloom, Amani; Tari, Farid Curves in the Minkowski plane and their contact with pseudo-circles. (English) Zbl 1267.53011 Geom. Dedicata 159, 109-124 (2012). Reviewer: Anton Gfrerrer (Graz) MSC: 53A35 58K05 53D12 × Cite Format Result Cite Review PDF Full Text: DOI
Reeve, Graham M.; Zakalyukin, Vladimir M. Singularities of the Minkowski set and affine equidistants for a curve and a surface. (English) Zbl 1253.58016 Topology Appl. 159, No. 2, 555-561 (2012). Reviewer: Maria Aparecida Soares Ruas (São Carlos) MSC: 58K05 58K40 53A15 × Cite Format Result Cite Review PDF Full Text: DOI
Alharbi, Fawaz Bifurcation diagrams and caustics of simple quasi border singularities. (English) Zbl 1250.58014 Topology Appl. 159, No. 2, 381-388 (2012). Reviewer: Raúl Oset Sinha (São Carlos) MSC: 58K05 58K40 53A15 × Cite Format Result Cite Review PDF Full Text: DOI
Sasaki, Takeshi; Yoshida, Masaaki Singularities of flat fronts and their caustics, and an example arising from the hyperbolic Schwarz map of a hypergeometric equation. (English) Zbl 1182.33009 Result. Math. 56, No. 1-4, 369-385 (2009). MSC: 33C05 53C42 58K05 × Cite Format Result Cite Review PDF Full Text: DOI
Chapman, S. J.; Howls, C. J.; King, J. R.; Olde Daalhuis, A. B. Why is a shock not a caustic? The higher-order Stokes phenomenon and smoothed shock formation. (English) Zbl 1135.34044 Nonlinearity 20, No. 10, 2425-2452 (2007). Reviewer: Nickolaj A. Lar’kin (Maringa) MSC: 34M60 35L70 × Cite Format Result Cite Review PDF Full Text: DOI Link
Van Manen, M. Maxwell strata and caustics. (English) Zbl 1143.58017 Brasselet, Jean-Paul (ed.) et al., Singularities in geometry and topology. Proceedings of the Trieste singularity summer school and workshop, ICTP, Trieste, Italy, August 15–September 3, 2005. Hackensack, NJ: World Scientific (ISBN 978-981-270-022-3/hbk). 787-824 (2007). Reviewer: Richárd Rimányi (Chapel Hill) MSC: 58K05 58K20 × Cite Format Result Cite Review PDF
Tabachnikov, Serge Geometry and billiards. (English) Zbl 1119.37001 Student Mathematical Library 30. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3919-5/pbk). xi, 176 p. (2005). Reviewer: Athanase Papadopoulos (Strasbourg) MSC: 37-01 51-01 37D50 37J10 78A05 70H05 82C05 00A09 00A05 × Cite Format Result Cite Review PDF Backlinks: MO
McCaffrey, D.; Banks, S. P. Lagrangian manifolds, viscosity solutions and Maslov index. (English) Zbl 0998.49017 J. Convex Anal. 9, No. 1, 185-224 (2002). MSC: 49L25 49L20 58E25 53D12 × Cite Format Result Cite Review PDF
Arnol’d, V. I. Astroidal geometry of hypercycloids and the Hessian topology of hyperbolic polynomials. (English. Russian original) Zbl 1058.58018 Russ. Math. Surv. 56, No. 6, 1019-1083 (2001); translation from Usp. Mat. Nauk 56, No. 6, 3-66 (2001). MSC: 58K05 58K20 57R17 58E05 53D99 × Cite Format Result Cite Review PDF
Glaeser, Georg Reflections on spheres and cylinders of revolution. (English) Zbl 1059.65503 J. Geom. Graph. 3, No. 2, 121-139 (1999). MSC: 65D18 53A04 68U05 51N05 × Cite Format Result Cite Review PDF Full Text: EuDML EMIS
Gorman, Arthur D. Addendum to a paper of Craig and Goodman. (English) Zbl 0810.35106 Int. J. Math. Math. Sci. 17, No. 4, 825-827 (1994). MSC: 35Q53 78A05 34E20 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Karadzhov, Georgi Asymptotic of the spectral function on the diagonal for a class of globally elliptic operators in \(\mathbb{R}{}^ n\). (Russian. English summary) Zbl 0787.35132 God. Sofij. Univ. “Kliment Okhridski”, Fak. Mat. Mekh. 80(1986), No. 1 (Mat.), 69-101 (1991). MSC: 35S05 47G30 35P20 × Cite Format Result Cite Review PDF
Gorman, Arthur D. Space-time caustics. (English) Zbl 0613.34046 Int. J. Math. Math. Sci. 9, 531-540 (1986). Reviewer: F.Jiang MSC: 34E20 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Shcherbak, I. G. Focal set of a surface with boundary, and caustics of groups generated by reflections \(B_ k\), \(C_ k\), and \(F_ 4\). (English) Zbl 0554.58017 Funct. Anal. Appl. 18, 84-85 (1984). MSC: 58C25 58K99 53A05 37J99 78A05 51F15 × Cite Format Result Cite Review PDF Full Text: DOI
Bruce, J. W.; Giblin, P. J. One-parameter families of caustics by reflexion in the plane. (English) Zbl 0547.58013 Q. J. Math., Oxf. II. Ser. 35, 243-251 (1984). Reviewer: E.Heil MSC: 58K35 58A40 53A04 57R70 78A05 × Cite Format Result Cite Review PDF Full Text: DOI
Bruce, J. W.; Giblin, P. J.; Gibson, C. G. Caustics through the looking glass. (English) Zbl 0547.58012 Math. Intell. 6, No. 1, 47-58 (1984). Reviewer: E.Heil MSC: 58K35 58A40 78A05 57R70 × Cite Format Result Cite Review PDF Full Text: DOI
Keller, H. B.; Perozzi, D. J. Fast seismic ray tracing. (English) Zbl 0538.73133 SIAM J. Appl. Math. 43, 981-992 (1983). MSC: 74L05 86A15 74J25 86-08 × Cite Format Result Cite Review PDF Full Text: DOI Link
Watson, J. G.; Siegmann, W. L.; Jacobson, M. J. Refracted ray characteristics from the geometrical spreading equation for depth-dependent media. (English) Zbl 0466.76072 J. Acoust. Soc. Am. 70, 583-590 (1981). MSC: 76Q05 × Cite Format Result Cite Review PDF Full Text: DOI