Constrained lagrangian submanifolds over singular constraining varieties and discriminant varieties
Annales de l'I.H.P. Physique théorique, Tome 46 (1987) no. 1, pp. 1-26. 
@article{AIHPA_1987__46_1_1_0,
     author = {Janeczko, Stanislaw},
     title = {Constrained lagrangian submanifolds over singular constraining varieties and discriminant varieties},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {1--26},
     publisher = {Gauthier-Villars},
     volume = {46},
     number = {1},
     year = {1987},
     mrnumber = {877993},
     zbl = {0611.58026},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1987__46_1_1_0/}
}
TY  - JOUR
AU  - Janeczko, Stanislaw
TI  - Constrained lagrangian submanifolds over singular constraining varieties and discriminant varieties
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1987
SP  - 1
EP  - 26
VL  - 46
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1987__46_1_1_0/
LA  - en
ID  - AIHPA_1987__46_1_1_0
ER  - 
%0 Journal Article
%A Janeczko, Stanislaw
%T Constrained lagrangian submanifolds over singular constraining varieties and discriminant varieties
%J Annales de l'I.H.P. Physique théorique
%D 1987
%P 1-26
%V 46
%N 1
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1987__46_1_1_0/
%G en
%F AIHPA_1987__46_1_1_0
Janeczko, Stanislaw. Constrained lagrangian submanifolds over singular constraining varieties and discriminant varieties. Annales de l'I.H.P. Physique théorique, Tome 46 (1987) no. 1, pp. 1-26. http://www.numdam.org/item/AIHPA_1987__46_1_1_0/

[1] R. Abraham, J.E. Marsden, Foundations of Mechanics, (2nd ed.), Benjaming (Cummings Reading), 1978. | MR

[2] V.I. Arnold, Singularities of ray systems. Proc. of the International congress of Mathematicians, Warszawa, 1983, p. 27-49. | MR | Zbl

[3] V.I. Arnol'D, Lagrangian varieties, asymptotic rays and the open swallowtail, Funct. Anal., t. 15, 1981, p. 1-14. | MR | Zbl

[4] S. Benenti, W.M. Tulczyjew, The geometrical meaning and globalization of the Hamilton-Jacobi method, Lecture Notes in Math., 863, 1980, p. 9-21. | MR | Zbl

[5] J.W. Bruce, Vector fields on discriminants and bifurcation varieties, Bull. London Math. Soc., t. 17, 1985, p. 257-262. | MR | Zbl

[6] J.W. Bruce, P. Giblin, Curves and Singularities, Cambridge Univ. Press, 1984. | MR | Zbl

[7] J. Damon, The unfolding and determinacy theorems for subgroups of A and K, Proc. of Symposia in Pure Math., t. 40, 1983, Part I, p. 233-254. | MR | Zbl

[8] A. Dimca, Function germs defined on isolated hypersurface singularities, Compositio Math., t. 53, 1984, p. 245-258. | Numdam | MR | Zbl

[9] P.A.M. Dirac, Generalized Hamiltonian Dynamics, Canad. J. Math., t. 2, 1950, p. 129-148. | MR | Zbl

[10] J.-J. Gervais, G-stability of mappings and stability of bifurcation diagrams, J. London Math. Soc., (2), t. 25, 1982, p. 551-563. | MR | Zbl

[11] C.G. Gibson, Singular points of smooth mappings, Research Notes in Math., t. 25, Pitman, 1979. | MR | Zbl

[12] M. Golubitsky, D.G. Schaeffer, A theory for imperfect bifurcation via singularity theory, Comm. Pure Appl. Math., t. 32, 1979, p. 21-98. | MR | Zbl

[13] M. Golubitsky, D.G. Schaeffer, A discussion of symmetry and symmetry breaking, Proc. of Symposia in Pure Math. A. M. S., t. 40, I, 1983, p. 499-515. | MR | Zbl

[14] K. Jänich, Caustics and catastrophes, Math. Ann., t. 209, 1974, p. 161-180. | MR | Zbl

[15] S. Janeczko, On algebraic criteria for k-determinacy of germs of functions on manifolds with boundary, Demonstratio Math., t. 15, 1982, p. 1113-1123. | MR | Zbl

[16] S. Janeczko, A note on singular lagrangian submanifolds, Journal of Geometry and Physics, t. 2, no. 3, 1985, p. 33-59. | MR | Zbl

[17] S. Janeczko, On stability of constrained lagrangian submanifolds, Bull. of the Polish Acad. of Sci. Math., t. 31, no. 5-8, 1983, p. 303-311. | MR | Zbl

[18] M. Kashiwara, Microlocal calculus, Lecture Notes in Physics, no. 39, Springer-Verlag, 1975. | MR

[19] M. Kashiwara, T. Kawai, T. Oshima, A study of Feynman integrals by micro-differential equations, Comm. Math. Phys., t. 60, 1978, p. 97-130. | MR | Zbl

[20] Nguyên Huu Dúc, Nguyên Tiên Dai, Stabilité de l'interaction géométrique entre deux composantes holonomes simples. Comptes Rendus Acad. Sci. Paris, t. A 291, 1980, p. 113. | Zbl

[21] Nguyên Tiên Dai, Nguyên Hũu Dúc, F. Pham, Singularités non dégénérées des systèmes de Gauss-Manin réticulés, Bull. Soc. Math. France, Mémoire, n° 6, 1981. | Numdam | Zbl

[22] F. Pham, Singularités des systèmes différentiels de Gauss-Manin, Progress in Math., t. 2, Birkhauser, 1979. | MR | Zbl

[23] D. Siersma, Singularities of functions on boundaries, corners, etc., Quart. J. Math. Oxford, (2), t. 32, 1981, p. 119-127. | MR | Zbl

[24] B. Teissier, The hunting of invariants in the geometry of discriminants, in Real and Complex Singularities, Oslo, 1976, Noordhoff-Sijthoff, 1977. | MR | Zbl

[25] W.M. Tulczyjew, The Legendre transformation, Ann. Inst. H. Poincaré, t. 27, n° 1, 1977, p. 101-114. | Numdam | MR | Zbl

[26] W.M. Tulczyjew, Control of static mechanical systems, in Dynamical Systems and Microphysics, Academic Press, 1984, p. 359-377. | MR | Zbl

[27] G. Wassermann, Stability of unfoldings in space and time, Acta Math., t. 135, 1975, p. 58-128. | MR | Zbl

[28] A. Weinstein, Lectures on Symplectic Manifolds, C. B. M. S., Conf. Series A. M. S., t. 29, 1977. | MR | Zbl

[29] V.M. Zakalyukin, On lagrangian and legendrian singularities. Funct. Anal. Appl., t. 10, 1976, p. 23-31. | Zbl