References

[A1]

Arnold, V.I., Singularities of smooth mappings, Uspekhi Mat. Neauk 23:1 (1968), 3-44 (= Russian Math. surveys 23:1 (1968), 1-43.)

[A2]

Arnold, V. I., Normal forms of functions near degenerate critical points; the Weyl groups A_k, D_k, E_k, and Lagrangian singularities, Funksional. Anal. i Prilozhen, 6:4 (1972), 3-25. (= Functional Anal. Appl. 6:4 (1972), 254-272.)

[A3]

Arnold, V.I., Critical points of smooth functions, Proc. Int. Cong. Math. vol. 1, Vancouver (1974), 19-37.

[A4]

Arnold, V. I., Mathematical Methods of Classical Mechanics, Moscow: Nauka (1974). English trans.: New York: Springer-Verlag (1978).

[A5]

Arnold, V. I., Advanced Ordinary Differential Equations, Moscow (1978).

[A6]

Arnold, V. I., Indices of singular points of 1-forms on a manifold with boundary, convolution of invariants of reflection groups, and singularities of projections of smooth surfaces, Uspekhi Mat. Nauk 34:2 (1979), 3-38. (= Russian Math. Surveys 34:2 (1979), 1-42.)

[A7]

Arnold, V. I., Some open problems in singularity theory, Geometry and Analysis (volume dedicated to K. Patody), Indian Academy of Sciences (1980).

[A8]

Arnold, V. I., Singularities of systems of rays, Uspekhi Mat. Nauk 38:2 (1983), 77-147. ( = Russian Math. Surveys 38:2 (1983), 87-176.)

[A9]

Arnold, V. I., Catastrophe Theory, second edition. New York: Springer-Verlag 1986.

[A10]

Arnold, V. I., Catastrophe Theory. Dyamical Systems V (V. I. Arnold, ed). New York: Springer-Verlag 1986, 207-271.

[A11]

Arnold, V. I., Singularities of Caustics and Wave Fronts. Dordrect: Kluwer 1990.

[A12]

Arnold, V. I., Topological problems of the theory of wave propagation, Uspekhi Mat. Nauk 51:1 (1996), 3-50. ( = Russian Math. Surveys 51 (1996), 1-47.)

[AGLV]

Arnold, V. I., Goryunov, V. V., Lyashko, O. V., and Vasiliev, V. A., Singularity Theory II, Classification and Applications. Dynamical Systems VIII (V. I. Arnold, ed.). New York: Springer-Verlag 1993.

[AGV]

Arnold, V. I., Guesein-Zade, S. M., and Varchenko, A. N., Singularities of Differentiable Mappings. Moscow: Nauka (1981). (English trans.: Boston: Birkhauser (1981).)

[Ba]

Banchoff, T. F., Computer animation and the geomtry of surfaces in 3- and 4-space, Proc. Int. Cong. Math. Helsinki (1978), 1005-1013.

[BaGM1]

Banchoff, T. F., Gaffney, T., and McCrory, C., Triple tangent planes of generic space curves, to appear.

[BaGM2]

Banchoff, T. F., Gaffney, T., and McCrory, C., Cusps of Gauss Mappings, Research Notes in Mathematics, 55, Pitman, London, 1982.

[BaT]

Banchoff, T. F. and Thom, R., Sur les points paraboliques des surfaces: erratum et complements, Comptes Rendues Acad. Sci. Paris t. 291 (27 October 1980), 503-505.

[BlW]

Bleeker, D. and Wilson, L., Stablility of Gauss maps, Illinois J. Math. 22(1978), 279-289.

[Bri1]

Brisgalova, L. N., Maximum functions of a family of functions depending on parameters, Funktsional. Anal. i Prilozhen 12:1 (1978), 66-67. (= Functional Anal. Appl. 12(1978), 50-51.)

[Bri2]

Brisgalova, L. N., Thesis, Moscow University, 1979.

[Bro]

Brodski, J. A., Diploma work, Moscow University, 1977.

[Bru1]

Bruce, J. W., The duals of generic hypersurfaces, preprint, University of Liverpool, 1979.

[Bru2]

Bruce, J. W., On singularities, envelopes and elementary differential geometry, Math. Proc. Camb. Phil. Soc. 89(1981), 43-48.

[Bru3]

Bruce, J. W., Generic geometry and duality, Singularities (J.-P. Brasselet, ed.), London Math. Soc. Lect. Notes 201 (1994), 29-59.

[BruG1]

Bruce, J. W., and Giblin, P. J., Generic geometry, Am. Math. Monthly 90 (1983), 529-545.

[BruG2]

Bruce, J. W., and Giblin, P. J., Outlines and their duals, Proc. London Math. Soc. (3) 50 (1985), 552-570.

[BruR]

Bruce, J. W., and Romero Fuster, M. C., Duality and orthogonal projections of curves and surfaces in Euclidean 3-space, Quart. J. Math. 42 (1991), 433-441.

[BruS]

Bruce, J. W., Seeing--the mathematical viewpoint, Math. Intelligencer 6:4 (1984), 18-25.

[BruT]

Bruce, J. W., Tari, F., Implicit differential equations from the singularity theory viewpoint, Singularities and Differential Equations, Banach Center Publ. 33, Warsaw: Polish Acad. Sci., 1996, 23-28.

[C1]

Callahan, J., Singularities and plane maps, Amer. Math. Monthly 81 (1974), 211-240.

[C2]

Callahan, J., Singularities and plane maps II: sketching catastrophes, Amer. Math. Monthly 84 (1977), 765-803.

[D]

David, J. M. S., Projection-generic curves, J. London Math. Soc. 27 (1983), 552-562.

[Da1]

Davidov, A. A., Singularities in two-dimensional control systems, Thesis, Moscow State University, 1982.

[Da2]

Davidov, A. A., Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular point, Funktsional. Anal. Prilozhen 19:2 (1985), 1-10. ( = Functional Anal. Appl. 19 (1985), 81-89.)

[F]

Freedman, M., Plans triply tangent to curves with non-vanishing torsion, Topology 19(1980), 1-8.

[GafR]

Gaffney, T. and Ruas, M., to appear.

[Gau]

Gauss, K. F., General investigations of curves surfaces. Hewlett, New York: Raven Press (1965).

[GolG]

Golubitsky, M., and Guillemin, V., Stable Mappings and their Singularities. New York: Springer-verlag (1973).

[Gor1]

Goryunov, V. V., Thesis, Moscow University, 1980.

[Gor2]

Goryunov, V. V., Simple projections of hypersurfaces, Doklady (1981).

[Gor3]

Goryunov, V. V., Singularities of projections of complete intersections, Contemporary Problems of Mathematics 22, Vinti, Moscow 1983, 167-206. ( = J. Soviet Math. 27 (1984), 2785-2811.)

[Gor4]

Goryunov, V. V. Singularities of projections. Singularity theory (Trieste 1993), River Edge: World Sci. Publ. 1995, 229-247.

[Gu]

Guckenheimer, J., The cusps of Zeeman's catastrophe machine, Topology 16 (1977), 177-180.

[HC]

Hilbert, D. and Cohn-Vossen, S., Geometry and the Imagination. New York: Chelsea (1952).

[Ke1]

Kergosien, Y. L., Singularite theorie des catastrophes, Lecture Notes of C. N. R. S. Atuem School of Theoretical Biology, chapter 8, Solignac, Sept. - Oct. 1980.

[Ke2]

Kergosien, Y. L., Geometrie de l'ensemble d'obturation d'un plongement multiprojectivement stable, Publication du departement de mathematiques de l'Universite Paris Val de Marne, to appear.

[Ke3]

Kergosien, Y. L., These de Mathematiques, Universite Paris VII, 1981.

[KeT]

Kergosien, Y. L. and Thom, R., Sur les points paraboliques des surfaces, Comptes Rendues Acad. Sci. Paris t. 299 (21 avril 1980), 705-710.

[Ko1]

Koenderink, J. J., Solid Shape. Cambridge, Mass.: MIT Press 1990.

[Ko2]

Koenderink, J. J., van Doorn, A. J., Illuminance critical points on generic smooth surfaces, J. Opt. Soc. Amer. A 10:5 (1993), 844-854.

[KoD]

Koenderink,, J. J. and van Doorn, A. J., The singularities of the visual mapping, Biol. Cybernetics 24 (1976), 51-59.

[Ku1]

Kulikov, V. S., Calculation of singularities of embeddings of generic algebraic surfaces in projective space P³, Funktsional. Anal. Prilozhen 17:3 (1983), 15-27. ( = Functional Anal. Appl. 17 (1983), 176-186.)

[Ku2]

Kulikov, V. S., On the number of special local centers of projection of an algebraic surface, Uspekhi Mat. Nauk 39:5 (1984), 245-246. ( = Russian Math. Surveys 39:5 (1984), 279-280.)

[Lak]

Lak, D., Singularities generiques des equations differentielles multiformes, Bol. Soc. Brasil. Math. 6 1975), 95-128.

[Lan]

Landis, E. E., Tangential singularities, Funktsional. Anal. i Prilozhen, 15 (1981).

[Le]

Levine, H., Stable maps: an introduction with low dimensional examples, Bol. Soc. Brasil. Mat. 7 (1976), 145-184.

[Lo]

Looijenga, E. J. N., Structural stability of smooth families of  functions, Thesis, Universiteit van Amsterdam, 1974.

[Ly1]

Lyashko, O. V., Thesis, Moscow University, 1979.

[Ly2]

Lyashko, O. V., Geometry of bifurcation diagrams, Uspekhi Mat. Nauk 34:3 (1979), 205-206. (= Russian Math. Surveys 34:3 (1979), 209-210.)

[Mar]

Martinet, J. Deploiments versels des applications differentiables et classification des applications stables, Singularites d'Applications Differentiables, Plans-sur-Bex 1975, Springer Lecture Notes in Math. 535 (1976), 1-44.

[Mat]

Mather, J., On Thom-Boardman singularities, Dynamical Systems, Peixoto, ed. New York: Academic Press (1973).

[Mc1]

McCrory, C., Profiles of Surfaces, preprint, University of Warwick 1980.

[Mc2]

McCrory, C., Generic curves and surfaces in 3-space: contact with lines and planes, preprint, University of Warwick 1980.

[McS]

McCrory, C., and Shifrin, T., Cusps of the projective Gauss map, J. Diff. Geom. 19 (1984), 257-276.

[Mi]

Milnor, J., Morse Theory, Annals of Math. Studies No. 51, Princeton (1963).

[Mon]

Montaldi, J. A., Surfaces in 3-space and their contact with circles, J. Diff. Geom. 23 (1986), 109-126.

[Mont]

Montesinos Amibilia, A., and Nuno Ballesteros, J. J., A knot without tritangent planes, Geometriae Dedicata 37 (1991), 141-153.

[Mori]

Morin, B., Formes canoniques des singularites d'une application differentiable, Comptes Rendues Acad. Sci. Paris 260 (1965), 5662-5665, 6503-6506.

[Moro]

Moron, H. R. and Mond, D., Closed curves with no quadrisecants, preprint, University of Liverpool, 1980.

[Mort]

Morton, H., Trefoil knots without tritangent planes, Bull. London Math. Soc. 23 (1991), 78-80.

[NMR]

Nuno Ballesteros, J. J., McCrory, C., and Romero Fuster, M. C., Self-translation surfaces, Matematica Contemporanea 5 (1993), 61-76.

[O]

Osawa, T., The numbers of triple tangencies of smooth space curves, Topology 24 (1985), 1-13.

[Pl1]

Platonova, O. A., Thesis, Moscow University, 1980.

[Pl2]

Platonova, O. A., Singularities of contact of a surface and a line, Uspekhi Mat. Nauk 36:1 (1981).

[Pl3]

Platonova, O. A., Singularities in the problem of an obstacle, Funcktsional. Anal. i. Prilozhen 15 (1981).

[Pl4]

Platonova, O. A., Shadow and terminator of a hypersurface of general position, Funktsional. Anal. Prilozhen 13:1 (1979), 77-78. ( = Functional Anal. Appl. 13 (1979), 64-65.)

[Pl5]

Platonova, O. A., Singularities of projection of smooth surfaces, Uspekhi Mat. Nauk 39:1 (1984), 149-150. ( = Russian Math. Surveys 39:1 (1984), 177-178.)

[Pl6]

Platonova, O. A., Projections of smooth surfaces, Trudy Sem. Petrovsk. 10 (1984), 135-149. ( = J. Soviet Math. 35 (1986), 2796-2808.)

[Por1]

Porteous, I. The normal singularities of a submanifold, J. Diff. Goem. 5 (1971), 543-564.

[Por2]

Porteous, I. R., Geometric Differentiation, for the Intelligence of Curves and Surfaces. Cambridge University Press 1994.

[PosS]

Poston, T. and Stewart, I., Catastrophe Theory and its Applications. London: Pitman (1978).

[RobR]

Robertson, S. A., and Romero Fuster, M. C., The convex hull of a hypersurface, Proc. London Math. Soc. (3) (1985), 370-384.

[Rom1]

Romero Fuster, Maria del Carmen, The convex hull of an immersion, Thesis, University of Southampton, 1981.

[Rom2]

Romero Fuster, M. C., Sphere stratifications and the Gauss map, Proc. Royal Soc. Edinburgh 95A (1983), 115-136.

[Rom3]

Romero Fuster, M. C., Generic embeddings, Gauss maps and stratifications, Springer Lecture Notes in Math. 1054 (1984), 164-181.

[Rom4]

Romero Fuster, M. C., Convexly generic surfaces in R³, Geometriae Dedicata 28 (1988), 7-29.

[RomS]

Romero-Fuster, M. C., Sedykh, V. D., A lower estimate for the number of zero-torsion points of a space curve, BeitrSge Algebra Geom. 38:1 (1997), 183-192.

[Sa]

Salmon, G., Analytic Geometry of Three Dimensions, vol. I (7th ed. 1927), vol III (5th ed. 1915). New York: Chelsea.

[Se1]

Sedych, V. D., Singularities of a convex hull of a curve in R³, Funktsional. Anal. i Prilozhen 11:1 (1977), 81-82. (= Functional Anal. Appl. 11:1 (1977), 72-73.)

[Se2]

Sedych, V. D., Thesis, Moscow University, 1981.

[Se3]

Sedykh, V. D., The structure of the convex hull of a space curve, Trudy Sem. Petrovsk. 6 (1981), 239-256.

[Se4]

Sedykh, V. D., Singularities of convex hulls, Sib. Mat. Zh. 24:3 (1983), 158-175. ( = Sib. Math. J. 24:3 (1983), 447-461.)

[Se5]

Sedykh, V. D., An infinitely smooth compact convex hypersurface whose shadow is not twice differentiable, Funktsional. Anal. Prilozhen 23:3 (1989), 86-87. ( = J. Soviet Math. 33 (1986), 1140-1153.)

[Se6]

Sedykh, V. D., Double tangent planes to a space curve, Sib. Mat. Zh. 30:1 (1989), 209-211. ( = Sib. Math. J. 30:1 (1989), 161-162.

[St]

Struik, D. Lectures on Classical Differential Geometry, 2nd ed. Reading, Massachusetts: Addison-Wesley (1961).

[T1]

Thom, R., Les singularites des applications differentiables, Ann. Inst. Fourier Grenoble 6 (1955-56), 43-87.

[T2]

Thom, R., Sur la theorie des enveloppes, Jour. Math. Pures Appl. 41 (1962), 177-192.

[T3]

Thom, R., Sur les equations differentielles multiformes et leurs integrales singulieres, Bol. Soc. Brasil. Mat. 3 (1972), 1-11.

[T4]

Thom, R. Stabilite Structurelle et Morphogenese. Reading, Massachusetts: Benjamin/Addison-Wesley (1973).

[Wa1]

Wall, C. T. C., Lectures on  stability and classification, Proc. Liverpool Singularities Symposium I, Springer Lecture Notes in Math. 192 (1971), 178-206.

[Wa2]

Wall, C. T. C., Geometric properties of generic differentiable manofolds, Geometry and Topology, Rio de Janeiro 1976, Springer Lecture Notes in Math. 597 (1977), 707-774.

[We]

Weinstein, A. Singularities in families of functions, Differential geometrie im Grossen, Berichte Math. Forsch. Oberwohlfach 4 (1971), 323-330.

[Wh]

Whitney, H., On singulartieies of mappings of Euclidean spaces I: Mappings of the plane in the plane, Ann. of Math. 62 (1955), 374-410.

[Wo]

Woodcock, A. E. R. and Psoton, T., A geometrical Study of the Elementary Catastrophes, Springer Lecture Notes in Math., 373 (1974).

[Z]

Zakalyukin, V. M., Singularities of convex hulls of smooth manifolds, Funksional. Anal. i. Prilozhen 11:3 (197), 76-77 (= Functional Anal. Appl. 11 (1977), 225-227.)