Caustique mystique

Bennequin, Daniel

Séminaire Bourbaki : volume 1984/85, exposés 633-650, Astérisque, no. 133-134 (1986), Exposé no. 634, 38 p.

MR Zbl | 4 citations dans Numdam

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     author = {Bennequin, Daniel},
     title = {Caustique mystique},
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Bennequin, Daniel. Caustique mystique, dans Séminaire Bourbaki : volume 1984/85, exposés 633-650, Astérisque, no. 133-134 (1986), Exposé no. 634, 38 p.. https://www.numdam.org/item/SB_1984-1985__27__19_0/

Bibliographie
Cité par

V. I. Arnold 1 - Normal form for functions near degenerate critical points, the Weyl groups Ak , Dk , Ek and lagrangian singularities, Funct. Anal. 27(1972) , 254- 272. | Zbl

V. I. Arnold 2 - 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

V. I. Arnold 3 - 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. | Zbl | MR

V. I. Arnold 4 - Singularities of systems of rays, Uspekhi Mat. Nauk 36(1983). | Zbl | MR

V. I. Arnold 5 - Singularities in variational calculus, Itogi Nauki, Contemporary problems in mathematics 22(1983), 3-55 (en russe). | MR

V. I. Arnold 6 - Catastrophe theory, Springer-Verlag, 1984. | Zbl | MR

V. I. Arnold 7 (avec A. N. Varchenko et S. M. Husein-Zade) - Singularities of maps, Nauka, Moscou, 1982 (en russe).

V. I. Arnold 8 - Singularities of Legendre varieties, of evolvents and of fronts at an obstacle, Ergodic theory and Dynamical systems 2(1982). | Zbl | MR

V. I. Arnold 9 - Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail, Funct. Anal. 15(1981), 235-246. | Zbl | MR

V. I. Arnold 10 - 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). | Zbl | MR

V. I. Arnold 11 - Méthodes mathématiques de la mécanique classique, MIR, Moscou, 1974. | Zbl | MR

V. I. Arnold 12 - Chapitres supplémentaires de la théorie des équations différentielles ordinaires, MIR, Moscou, 1978. | Zbl | MR

V. I. Arnold 13 - Wave front evolution and equivariant Morse lemma, Comm. on Pure and Appl. Math. 29(1976), 557-582. | Zbl | MR

V. I. Arnold 14 - A spectral sequence for the reduction of function to normal forms, Funct. Anal. 9(1975), 251-253. | Zbl | MR

V. I. Arnold 15 - Singularities of ray-systems, Comm. I.C.M. 1983, Varsovie. | Zbl | MR

M. Artin - On isolated rational singularities of surfaces, Amer. J. of Math. 88 (1966), 23-58. | Zbl | MR

J. Bernoulli - Lectiones math. methodo integralium (transcrites par L'Hospital) , Paris, 1691.

N. Bourbaki - Groupes et algèbres de Lie, chapitres 4, 5 et 6, Masson, Paris, 1981. | Zbl | MR

E. Brieskorn 1 - Singular elements of semi-simple algebraic groups, Proc. I.C.M. Nice 2(1970), 279-284. | Zbl | MR

E. Brieskorn 2 - Über die Auflösung gewisser singularitäten von holomorphen Abbildungen, Math. Annalen 166(1966), 76-102. | Zbl | MR

J. W. Bruce 1 - Seeing, the mathematical view-point, Math. Intellig. 6 (1984) , 18-25. | Zbl | MR

J. W. Bruce 2 - Projections and reflections of generic surfaces in R3, Math. Scandinavia, 1984. | Zbl

C. Carathdodory - Variations rechnung und partielle Differentialgleichungen erster ordnung, Teubner, Leipzig, u. Berlin, 1935. | JFM

A. Cayley 1 - Memoirs on Quantics, in Oeuvres complètes.

A. Cayley 2 - On systems of rays, Messenger of Math. 17(1888), 73-78. | JFM

A. Cayley 3 - Memoirs on Caustics, in Oeuvres complètes.

A. Chenciner - Singularités des fonctions différentiables, Encycl. Universalis, 1984.

C. Chevalley - Invariants of finite groups generated by reflections, Amer. J. of Math. 77(1955), 778-782. | Zbl | MR

H. S. M. Coxeter 1 - Introduction to Geometry, 2e édition, Wiley & Sonc, inc., 1969. | Zbl | MR

H. S. M. Coxeter 2 - Regular polytopes, 2e édition, Dover, 1973. | MR

H. S. M. Coxeter and W. O. J. Moser - Generators and relations for discrete groups, Ergebnisse 14, Springer-Verlag (4e édition), 1980. | Zbl | MR

M. Demazure - 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. | Zbl | MR | Numdam

N. H. Duc et N. Z. Dai - Stabilité de l'interaction géométrique entre deux composantes holonomes simples, Note C.R.A.S., Paris, t. 291(1980), 113-116. | Zbl

J. J. Duistermaat 1 - Oscillatory integrals, Lagrange immersions, and unfolding of singularities, Comm. in Pure and Appl. Math. 27(1974), 207-281. | Zbl | MR

J. J. Duistermaat 2 - The light in the neighborhood of a caustic, Sém. Bourbaki 1976-77, exp. 490, Springer-Verlag, Lect. Notes in Math. 677(1978), 19-29. | Zbl | MR | Numdam

A. Dürer - ... Geometricarum libris..., Paris, 1532.

P. Du Val - On isolated singularities of surfaces which do not affect the conditions of adjunction, Proc. Cambridge Philos. Soc. 30(1934), 483-491. | Zbl

L. Fejes-Toth - Reguläre Figuren, Budapest, 1965. | Zbl | MR

T. Gaffmey - The structure of TA(f), Proc. A.M.S. 401(1983), 409-427.

J. Guckenheimer - Catastrophes and PPE, Ann. Inst. Fourier 23(1973), 31-59. | Zbl | MR | Numdam

V. Guillemin and S. Sternberg - Geometric asymptotics, AMS Math. Surveys 14, 1977. | Zbl | MR

A. B. Guivental 1 - Manifolds of polynomials having a root of fixed multiplicity, and the generalized Newton equation, Funct. Anal. 16 (1982) , 10-14. | Zbl

A. B. Guivental 2 - Variétés lagrangiennes, singulières et SL2-modules irréductibles, Uspekhi Math. Nauk (1982), 109-110 (en russe).

A.B. Guivental and A. N. Varchenko - Mapping of periods and intersection form, Funct. Anal. 16(1982), 82-93. | Zbl

W. R. Hamilton - "Theory of system of rays", Trans. R.I. Acad. 15(1828), 69-174.

D. Hilbert und S. Cohn-Vossen - Anschauliche Geometric, Berlin, Springer, 1932. | JFM

M. De L'Hospital - "Analyse des infiniment petits", 2e édition, Paris, 1775.

L. Hörmander - Fourier integral operators I, Acta Math. 127(1971), 79-183. | Zbl | MR

C. Huygens 1 - De motu pendulorum, Paris, 1673, (réédition, Bruxelles, 1966).

C. Huygens 2 - Traité de la lumière, Leide, 1690 (réédition, Bruxelles, 1967). | JFM

J. Kepler - Opera Omnia (édit. Ch. Frisch).

F. Klein - Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen von fünften Grade, Teubner, Leipzig, 1884. | Zbl | JFM

L. Landau, E. Lifschitz - Mécanique classique, MIR, 1966.

E. E. Landis - Tangential singularities, Funct. Anal. 15(1981), 103-114. | Zbl | MR

E. J. N. Looijenga 1 - Isolated singular points on complete intersection, Cambridge LN 77, 1984. | Zbl | MR

E. J. N. Looijenga 2 - A period mapping for certain semi-universal de formations, Comp. Math. 30(1974), 299-316. | Zbl | MR | Numdam

E. J. N. Looijenga 3 - The discriminant of a real simple singularity, Comp. Math. 37 (1978), 51-62. | Zbl | MR | Numdam

O. V. Lyashko 1 - The geometry of bifurcation diagrams, Itoki Nauki, Contemporary problems in Math. 22(1983), 94-129. | Zbl | MR

O. V. Lyashko 2 - Classification of critical points of functions on a manifold with singular boundary, Funct. Anal. 17(1983), 187-303. | Zbl | MR

J. Mc Kay - Cartan matrices, finite groups of quaternions, and kleinian singularities, Proc. A.M.S. (1981), 153-154. | Zbl | MR

M. Malus - Traité d'optique, Mémoires de l'Institut des Sciences ... , tome 2, Paris, 1811, 214-302.

Théorie de la double réfraction, loc. cit., 303-508.

J. Martinet - Singularities of smooth functions and maps, Cambridge Univ. Press 58 (1982) . | Zbl | MR

J. Mather - Stability of C∞ mappings I, II, Ann. of Math. 87(1968), 89-104, et 89 (1969), 254-291. | Zbl

V. I. Matov - Unimodal and bimodal germs of functions on a manifold with boundary, Trudy Sem. Petrowsky 7(1981), 174-189. | Zbl | MR

R. B. Melrose 1 - Equivalence of glancing hypersurfaces, Invent. Math. 37(1976), 165-191. | Zbl | MR

R. B. Melrose 2 - Equivalence of glancing hypersurfaces II, Math. Annalen 255(1981), 159-198. | Zbl | MR

J. Milnor 1 - Singular points of complex hypersurfaces, Ann. Math. Studies 61, Princeton, 1968. | Zbl | MR

J. Milnor 2 - On the 3-dimensional Brieskorn manifolds M(p,q,r), in "Knots, groups and 3-manifolds", Princeton (1975), 175-225. | Zbl | MR

B. Morin - Formes canoniques des singularités d'une application différentiable, C.R.A.S. (Paris) (1965) 250 III, 5662-5665 & 6503-6506. | Zbl

D. Mumford - Curves and their jacobians - Michigan Press, 1975. | Zbl | MR

O. A. Platonova 1 - Singularities of systems of rays near an obstruction, VINITI (1981), 647-681.

O. A. Platonova 2 - Singularities of the disposition of a surface and a live, Uspekhi Math. Nauk 36(1981). | Zbl | MR

O. A. Platonova 3 - Singularities in the problem of the quickest way round an obstacle, Funct. Anal. 15(1981), 147-148. | Zbl | MR

I.R. Porteous - The normal singularities of a submanifold, J. Diff. Geometry 5 (1971), 543-564. | Zbl | MR

K. Saito - Primitive forms for a universal unfolding of a function with an isolated critical point, J. Fac. Sci. Univ. Tokyo 29(1982). | Zbl | MR

I. G. Scherback - 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

O. P. Scherback 1 -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

O. P. Scherback 2 - Projectively dual space curves and legendrian singularities, Trudy Tbilisi 13-14(1982). | Zbl

I. Schur und H. Grunsky - Vorlesungen über Invariantentheorie, Springer-Verlag, Grundlehren bd 143, 1968. | Zbl | MR

P. Slodowy 1 - Four lectures on simple groups and singularities, Comm. Math. Inst. Rijksuniversiteit Utrecht 11(1980). | Zbl | MR

P. Slodowy 2 - Simple singularities and simple algebraic groups, Springer-Verlag, Lect. Notes in Math. 815(1980). | Zbl | MR

P. Slodowy 3 - Eine bewerkungen zur Entfaltung symmetrischen Funktionen, Math. Zeitschrift 158(1978), 157-170. | Zbl | MR

T. A. Springer - Invariant theory, Springer-Verlag, Lect. Notes in Math. 585, 1977. | Zbl | MR

R. Thom 1 - Stabilité structurelle et morphogénèse, Benjamin, 1972. | Zbl | MR

R. Thom 2 - Modèles mathématiques de la morphogénèse, nouvelle édition, Bourgois, 1980.

R. Thom 3 - Sur la théorie des enveloppes, J. Math. Pures et Appl. 41(1962), 177- 192. | Zbl | MR

G. N. Tjurina - Resolution of singularities of plane deformation of double rational points, Funct. Anal. 4(1970), 68-73. | Zbl | MR

E. Von Tschirnhausen - Actes de Leipsick, novembre 1682.

A. N. Varchenko - Asymptotic mixed Hodge structures in the vanishing cohomology, Izvetjia 45(1981), 540-591. | Zbl | MR

C.T.C. Wall - Geometric properties of generic differentiable manifolds, Springer-Verlag, Lect. Notes in Math. 597(1977), 707-774. | Zbl | MR

A. Weinstein 1 - Lectures on symplectic manifolds, Conf. Board of the Math. Sci. AMS 29(1976). | Zbl | MR

A. Weinstein 2 - Symplectic manifolds and their lagrangian submanifolds, Advanœs in Math. 6(1977), 329-346. | Zbl

A. Weinstein 3 - Singularities of families of functions, Bibl. Institut Manhein, 1971. | MR

H. Weyl - Symmetry, Princeton Univ. Press, 1952. | Zbl | MR

H. Whitney - On singularities of mappings of Euclidian spaces I. Mapping of the plane into the plane, Ann. of Math. 62(1955), 374-410. | Zbl | MR

I. Zakalyukin 1 - Lagrangian and legendrian singularities, Funct. Anal. 10(1976), 23-31. | Zbl

I. Zakalyukin 2 - Bifurcation of front, caustics depending on a parameter, Itogi Nauki 22(1983), 53-93 (en russe).

C. Zeeman - Catastroph theory, Selected papers 1972-77, Addison Wesley, 1977. | Zbl