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1999 | 50 | 1 | 123-135
Tytuł artykułu

Determinacy, transversality and Lagrange stability

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Tom
50
Numer
1
Strony
123-135
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
Bibliografia
  • [1] V. I. Arnol'd, Normal forms of functions near degenerate critical points, the Weyl groups of $A_k$, $D_k$, $E_k$, and Lagrangian singularities (in Russian), Funktsional. Anal. i Prilozhen. 6 (1972), no. 4, 3-25; English transl.: Funct. Anal. Appl. 6 (1972), 254-272.
  • [2] V. I. Arnol'd, Lagrangian manifolds with singularities, asymptotic rays, and the open swallowtail (in Russian), Funktsional. Anal. i Prilozhen. 15 (1981), no. 4, 1-14; English transl.: Funct. Anal. Appl. 15 (1981), 235-246.
  • [3] V. I. Arnol'd, Singularities of Caustics and Wave Fronts, Math. Appl. (Soviet Ser.) 62, Kluwer Academic Publ., Dordrecht, 1990.
  • [4] V. I. Arnol'd, S. M. Guseĭn-Zade, A. N. Varchenko, Singularities of Differentiable Maps I, Monogr. Math. 82, Birkhäuser, Boston, 1985.
  • [5] J. Damon, The unfolding and determinacy theorems for subgroups of A and K, Mem. Amer. Math. Soc. 50 (1984), no. 306.
  • [6] A. B. Givental', Lagrangian imbeddings of surfaces and the open Whitney umbrella (in Russian), Funktsional. Anal. i Prilozhen. 20 (1986), no. 3, 35-41; English transl.: Funct. Anal. Appl. 20 (1986), 197-203.
  • [7] A. B. Givental', Singular Lagrangian manifolds and their Lagrangian mappings (in Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Ser. Sovremennye Problemy Matematiki 33, VINITI, Moscow, 1988, 55-112; English transl.: J. Soviet Math. 52 (1990), 3246-3278.
  • [8] M. Golubitsky, V. Guillemin, Contact equivalence for Lagrangian manifolds, Adv. Math. 15 (1975), 357-387.
  • [9] G. Ishikawa, Families of functions dominated by distributions of C-classes of map-germs, Ann. Inst. Fourier (Grenoble) 33 (1983), 199-217.
  • [10] G. Ishikawa, The local model of an isotropic map-germ arising from one dimensional symplectic reduction, Math. Proc. Cambridge Philos. Soc. 111 (1992), 103-112.
  • [11] G. Ishikawa, Parametrization of a singular Lagrangian variety, Trans. Amer. Math. Soc. 331 (1992), 787-798.
  • [12] G. Ishikawa, Parametrized Legendre and Lagrange varieties, Kodai Math. J. 17 (1994), 442-451.
  • [13] G. Ishikawa, Transversalities for Lagrange singularities of isotropic mappings of corank one, in: Singularities and Differential Equations, S. Janeczko, W. Zajączkowski and B. Ziemian (eds.), Banach Center Publ. 33, Warsaw, 1996, 93-104.
  • [14] G. Ishikawa, Symplectic and Lagrange stabilities of open Whitney umbrellas, Invent. Math. 126 (1996), 215-234.
  • [15] S. Janeczko, Generating families for images of Lagrangian submanifolds and open swallowtails, Math. Proc. Cambridge Philos. Soc. 100 (1986), 91-107.
  • [16] B. Malgrange, Ideals of Differentiable Functions, Oxford Univ. Press, London, 1966.
  • [17] B. Malgrange, Frobenius avec singularités. 2. Le cas général, Invent. Math. 39 (1977), 67-89.
  • [18] J. N. Mather, Stability of $C^∞$ mappings. I: The division theorem, Ann. of Math. (2) 87 (1968), 89-104. II: Infinitesimal stability implies stability, Ann. of Math. (2) 89 (1969), 254-291. III: Finitely determined map-germs, Inst. Hautes Études Sci. Publ. Math. 35 (1968), 127-156. IV: Classification of stable germs by R algebras, Inst. Hautes Études Sci. Publ. Math. 37 (1970), 223-248. V: Transversality, Adv. Math. 4 (1970), 301-336. VI: The nice dimensions, in: Proceedings of Liverpool Singularities-Symposium, I (1969/70), Lecture Notes in Math. 192, Springer, Berlin, 1971, 207-253.
  • [19] J. N. Mather, S. S.-T. Yau, Classification of isolated hypersurface singularities by their moduli algebras, Invent. Math. 69 (1982), 243-251.
  • [20] D. Mond, Deformations which preserve the non-immersive locus of a map-germ, Math. Scand. 66 (1990), 21-32.
  • [21] A. du Plessis, L. Wilson, On right-equivalence, Math. Z. 190 (1985), 163-205.
  • [22] O. P. Shcherbak, Wave fronts and reflection groups (in Russian), Uspekhi Mat. Nauk 43 (1988), no. 3, 125-160; English transl.: Russian Math. Surveys 43 (1988), no. 3, 149-194.
  • [23] T. Tsukada, unpublished note.
  • [24] C. T. C. Wall, Finite determinacy of smooth map-germs, Bull. London Math. Soc. 13 (1981), 481-539.
  • [25] S. S.-T. Yau, Criteria for right-left equivalence and right equivalence of holomorphic functions with isolated critical points, Proc. Sympos. Pure Math. 41 (1984), 291-297.
  • [26] V. M. Zakalyukin, Lagrangian and Legendre singularities (in Russian), Funktsional. Anal. i Prilozhen. 10 (1976), no. 1, 26-36; English transl.: Funct. Anal. Appl. 10 (1976), no. 1, 23-31.
  • [27] V. M. Zakalyukin, Generating ideals of Lagrangian varieties, in: Theory of Singularities and its Applications, V. I. Arnol'd (ed.), Adv. Soviet Math. 1, Amer. Math. Soc., Providence, 1990, 201-210.
  • [28] V. M. Zakalyukin, R. M. Roberts, Stability of Lagrangian manifolds with singularities (in Russian), Funktsional. Anal. i Prilozhen. 26 (1992), no. 3, 28-34; English transl.: Funct. Anal. Appl. 26 (1992), 174-178.
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Bibliografia
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