@incollection{SB_1984-1985__27__19_0, author = {Bennequin, Daniel}, title = {Caustique mystique}, booktitle = {S\'eminaire Bourbaki : volume 1984/85, expos\'es 633-650}, series = {Ast\'erisque}, note = {talk:634}, pages = {19--56}, publisher = {Soci\'et\'e math\'ematique de France}, number = {133-134}, year = {1986}, mrnumber = {837213}, zbl = {0632.58011}, language = {fr}, url = {http://www.numdam.org/item/SB_1984-1985__27__19_0/} }
TY - CHAP AU - Bennequin, Daniel TI - Caustique mystique BT - Séminaire Bourbaki : volume 1984/85, exposés 633-650 AU - Collectif T3 - Astérisque N1 - talk:634 PY - 1986 SP - 19 EP - 56 IS - 133-134 PB - Société mathématique de France UR - http://www.numdam.org/item/SB_1984-1985__27__19_0/ LA - fr ID - SB_1984-1985__27__19_0 ER -
%0 Book Section %A Bennequin, Daniel %T Caustique mystique %B Séminaire Bourbaki : volume 1984/85, exposés 633-650 %A Collectif %S Astérisque %Z talk:634 %D 1986 %P 19-56 %N 133-134 %I Société mathématique de France %U http://www.numdam.org/item/SB_1984-1985__27__19_0/ %G fr %F SB_1984-1985__27__19_0
Bennequin, Daniel. Caustique mystique, dans Séminaire Bourbaki : volume 1984/85, exposés 633-650, Astérisque, no. 133-134 (1986), Exposé no. 634, 38 p. http://www.numdam.org/item/SB_1984-1985__27__19_0/
Normal form for functions near degenerate critical points, the Weyl groups Ak , Dk , Ek and lagrangian singularities, Funct. Anal. 27(1972) , 254- 272. | Zbl
1 -Critical points of smooth functions and their normal forms, Uspekhi Mat. Nauk 30(1975), 3-65. Russian Math. Surveys (n° 5), p. 1-75. | MR
2 -Critical points of functions on a manifold with boundary, the simple Lie groups Bk , Ck , F4 and singularities of evolutes, Uspekhi Mat. Nauk 33 (II) (1978), 91-107. Russian Math. Surveys (n° 5) , p. 99-116. | MR | Zbl
3 -Singularities of systems of rays, Uspekhi Mat. Nauk 36(1983). | MR | Zbl
4 -Singularities in variational calculus, Itogi Nauki, Contemporary problems in mathematics 22(1983), 3-55 (en russe). | MR
5 -Catastrophe theory, Springer-Verlag, 1984. | MR | Zbl
6 -Singularities of maps, Nauka, Moscou, 1982 (en russe).
7 (avec et ) -Singularities of Legendre varieties, of evolvents and of fronts at an obstacle, Ergodic theory and Dynamical systems 2(1982). | MR | Zbl
8 -Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail, Funct. Anal. 15(1981), 235-246. | MR | Zbl
9 -Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups and singular projections of smooth surfaces, Uspekhi Mat. Nauk 34(1979). | MR | Zbl
10 -Méthodes mathématiques de la mécanique classique, MIR, Moscou, 1974. | MR | Zbl
11 -Chapitres supplémentaires de la théorie des équations différentielles ordinaires, MIR, Moscou, 1978. | MR | Zbl
12 -Wave front evolution and equivariant Morse lemma, Comm. on Pure and Appl. Math. 29(1976), 557-582. | MR | Zbl
13 -A spectral sequence for the reduction of function to normal forms, Funct. Anal. 9(1975), 251-253. | MR | Zbl
14 -Singularities of ray-systems, Comm. I.C.M. 1983, Varsovie. | MR | Zbl
15 -On isolated rational singularities of surfaces, Amer. J. of Math. 88 (1966), 23-58. | MR | Zbl
-Lectiones math. methodo integralium (transcrites par L'Hospital) , Paris, 1691.
-Groupes et algèbres de Lie, chapitres 4, 5 et 6, Masson, Paris, 1981. | MR | Zbl
-Singular elements of semi-simple algebraic groups, Proc. I.C.M. Nice 2(1970), 279-284. | MR | Zbl
1 -Über die Auflösung gewisser singularitäten von holomorphen Abbildungen, Math. Annalen 166(1966), 76-102. | MR | Zbl
2 -Seeing, the mathematical view-point, Math. Intellig. 6 (1984) , 18-25. | MR | Zbl
1 -Projections and reflections of generic surfaces in R3, Math. Scandinavia, 1984. | Zbl
2 -Variations rechnung und partielle Differentialgleichungen erster ordnung, Teubner, Leipzig, u. Berlin, 1935. | JFM
-Memoirs on Quantics, in Oeuvres complètes.
1 -On systems of rays, Messenger of Math. 17(1888), 73-78. | JFM
2 -Memoirs on Caustics, in Oeuvres complètes.
3 -Singularités des fonctions différentiables, Encycl. Universalis, 1984.
-Invariants of finite groups generated by reflections, Amer. J. of Math. 77(1955), 778-782. | MR | Zbl
-Introduction to Geometry, 2e édition, Wiley & Sonc, inc., 1969. | MR | Zbl
1 -Regular polytopes, 2e édition, Dover, 1973. | MR
2 -Generators and relations for discrete groups, Ergebnisse 14, Springer-Verlag (4e édition), 1980. | MR | Zbl
and -Classification des germes à point critique isolé et à nombre de modules 0 ou 1 (d'après V.I. Arnold), Sém. Bourbaki 1973-74, exp. 443, Springer-Verlag, Lect. Notes in Math. 431(1975), 124-142. | Numdam | MR | Zbl
-Stabilité de l'interaction géométrique entre deux composantes holonomes simples, Note C.R.A.S., Paris, t. 291(1980), 113-116. | Zbl
et -Oscillatory integrals, Lagrange immersions, and unfolding of singularities, Comm. in Pure and Appl. Math. 27(1974), 207-281. | MR | Zbl
1 -The light in the neighborhood of a caustic, Sém. Bourbaki 1976-77, exp. 490, Springer-Verlag, Lect. Notes in Math. 677(1978), 19-29. | Numdam | MR | Zbl
2 -... Geometricarum libris..., Paris, 1532.
-On isolated singularities of surfaces which do not affect the conditions of adjunction, Proc. Cambridge Philos. Soc. 30(1934), 483-491. | Zbl
-Reguläre Figuren, Budapest, 1965. | MR | Zbl
-The structure of TA(f), Proc. A.M.S. 401(1983), 409-427.
-Catastrophes and PPE, Ann. Inst. Fourier 23(1973), 31-59. | Numdam | MR | Zbl
-Geometric asymptotics, AMS Math. Surveys 14, 1977. | MR | Zbl
and -Manifolds of polynomials having a root of fixed multiplicity, and the generalized Newton equation, Funct. Anal. 16 (1982) , 10-14. | Zbl
1 -Variétés lagrangiennes, singulières et SL2-modules irréductibles, Uspekhi Math. Nauk (1982), 109-110 (en russe).
2 -Mapping of periods and intersection form, Funct. Anal. 16(1982), 82-93. | Zbl
and -Theory of system of rays", Trans. R.I. Acad. 15(1828), 69-174.
- "Anschauliche Geometric, Berlin, Springer, 1932. | JFM
und -Analyse des infiniment petits", 2e édition, Paris, 1775.
- "Fourier integral operators I, Acta Math. 127(1971), 79-183. | MR | Zbl
-De motu pendulorum, Paris, 1673, (réédition, Bruxelles, 1966).
1 -Traité de la lumière, Leide, 1690 (réédition, Bruxelles, 1967). | JFM
2 -Opera Omnia (édit. Ch. Frisch).
-Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen von fünften Grade, Teubner, Leipzig, 1884. | JFM | Zbl
-Mécanique classique, MIR, 1966.
, -Tangential singularities, Funct. Anal. 15(1981), 103-114. | MR | Zbl
-Isolated singular points on complete intersection, Cambridge LN 77, 1984. | MR | Zbl
1 -A period mapping for certain semi-universal de formations, Comp. Math. 30(1974), 299-316. | Numdam | MR | Zbl
2 -The discriminant of a real simple singularity, Comp. Math. 37 (1978), 51-62. | Numdam | MR | Zbl
3 -The geometry of bifurcation diagrams, Itoki Nauki, Contemporary problems in Math. 22(1983), 94-129. | MR | Zbl
1 -Classification of critical points of functions on a manifold with singular boundary, Funct. Anal. 17(1983), 187-303. | MR | Zbl
2 -Cartan matrices, finite groups of quaternions, and kleinian singularities, Proc. A.M.S. (1981), 153-154. | MR | Zbl
-Traité d'optique, Mémoires de l'Institut des Sciences ... , tome 2, Paris, 1811, 214-302.
-Théorie de la double réfraction, loc. cit., 303-508.
Singularities of smooth functions and maps, Cambridge Univ. Press 58 (1982) . | MR | Zbl
-Stability of C∞ mappings I, II, Ann. of Math. 87(1968), 89-104, et 89 (1969), 254-291. | Zbl
-Unimodal and bimodal germs of functions on a manifold with boundary, Trudy Sem. Petrowsky 7(1981), 174-189. | MR | Zbl
-Equivalence of glancing hypersurfaces, Invent. Math. 37(1976), 165-191. | MR | Zbl
1 -Equivalence of glancing hypersurfaces II, Math. Annalen 255(1981), 159-198. | MR | Zbl
2 -Singular points of complex hypersurfaces, Ann. Math. Studies 61, Princeton, 1968. | MR | Zbl
1 -On the 3-dimensional Brieskorn manifolds M(p,q,r), in "Knots, groups and 3-manifolds", Princeton (1975), 175-225. | MR | Zbl
2 -Formes canoniques des singularités d'une application différentiable, C.R.A.S. (Paris) (1965) 250 III, 5662-5665 & 6503-6506. | Zbl
-Curves and their jacobians - Michigan Press, 1975. | MR | Zbl
-Singularities of systems of rays near an obstruction, VINITI (1981), 647-681.
1 -Singularities of the disposition of a surface and a live, Uspekhi Math. Nauk 36(1981). | MR | Zbl
2 -Singularities in the problem of the quickest way round an obstacle, Funct. Anal. 15(1981), 147-148. | MR | Zbl
3 -I.The normal singularities of a submanifold, J. Diff. Geometry 5 (1971), 543-564. | MR | Zbl
-Primitive forms for a universal unfolding of a function with an isolated critical point, J. Fac. Sci. Univ. Tokyo 29(1982). | MR | Zbl
-Focal set of a surface with boundary, on caustics of groups generated by reflection Bk , Ck and F4 , Funct. Anal. 18(1984), 84-85. | Zbl
-Singularities of families of evolvents in the neighborhood of an inflection point of the curve, and the group H3 generated by reflections, Funct. Anal. 17(1983), 301-302. | Zbl
1 -Projectively dual space curves and legendrian singularities, Trudy Tbilisi 13-14(1982). | Zbl
2 -Vorlesungen über Invariantentheorie, Springer-Verlag, Grundlehren bd 143, 1968. | MR | Zbl
und -Four lectures on simple groups and singularities, Comm. Math. Inst. Rijksuniversiteit Utrecht 11(1980). | MR | Zbl
1 -Simple singularities and simple algebraic groups, Springer-Verlag, Lect. Notes in Math. 815(1980). | MR | Zbl
2 -Eine bewerkungen zur Entfaltung symmetrischen Funktionen, Math. Zeitschrift 158(1978), 157-170. | MR | Zbl
3 -Invariant theory, Springer-Verlag, Lect. Notes in Math. 585, 1977. | MR | Zbl
-Stabilité structurelle et morphogénèse, Benjamin, 1972. | MR | Zbl
1 -Modèles mathématiques de la morphogénèse, nouvelle édition, Bourgois, 1980.
2 -Sur la théorie des enveloppes, J. Math. Pures et Appl. 41(1962), 177- 192. | MR | Zbl
3 -Resolution of singularities of plane deformation of double rational points, Funct. Anal. 4(1970), 68-73. | MR | Zbl
-Actes de Leipsick, novembre 1682.
-Asymptotic mixed Hodge structures in the vanishing cohomology, Izvetjia 45(1981), 540-591. | MR | Zbl
-Geometric properties of generic differentiable manifolds, Springer-Verlag, Lect. Notes in Math. 597(1977), 707-774. | MR | Zbl
-Lectures on symplectic manifolds, Conf. Board of the Math. Sci. AMS 29(1976). | MR | Zbl
1 -Symplectic manifolds and their lagrangian submanifolds, Advanœs in Math. 6(1977), 329-346. | Zbl
2 -Singularities of families of functions, Bibl. Institut Manhein, 1971. | MR
3 -Symmetry, Princeton Univ. Press, 1952. | MR | Zbl
-On singularities of mappings of Euclidian spaces I. Mapping of the plane into the plane, Ann. of Math. 62(1955), 374-410. | MR | Zbl
-Lagrangian and legendrian singularities, Funct. Anal. 10(1976), 23-31. | Zbl
1 -Bifurcation of front, caustics depending on a parameter, Itogi Nauki 22(1983), 53-93 (en russe).
2 -Catastroph theory, Selected papers 1972-77, Addison Wesley, 1977. | Zbl
-