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1999 | 50 | 1 | 151-161
Tytuł artykułu

Invariant properties of the generalized canonical mappings

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
One of the fundamental objectives of the theory of symplectic singularities is to study the symplectic invariants appearing in various geometrical contexts. In the paper we generalize the symplectic cohomological invariant to the class of generalized canonical mappings. We analyze the global structure of Lagrangian Grassmannian in the product symplectic space and describe the local properties of generic symplectic relations.
Słowa kluczowe
Rocznik
Tom
50
Numer
1
Strony
151-161
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Institute of Mathematics, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
Bibliografia
  • [1] V. I. Arnol'd, S. M. Guseĭn-Zade, A. N. Varchenko, Singularities of Differentiable Maps I, Monogr. Math. 82, Birkhäuser, Boston, 1985.
  • [2] A. P. Fordy, A. B. Shabat, and A. P. Veselov, Factorization and Poisson correspondences, Teoret. Mat. Fiz. 105:2 (1995), 225-245; reprinted in: Theoret. and Math. Phys. 105 (1995), 1369-1386.
  • [3] V. Guillemin, R. B. Melrose, A cohomological invariant of discrete dynamical systems, in: E. B. Christoffel. The influence of his work on mathematics and the physical sciences, P. L. Butzer and F. Fehér (eds.), Birkhäuser, Basel, 1981, 672-679.
  • [4] V. Guillemin, S. Sternberg, Some problems in integral geometry and some related problems in micro-local analysis, Amer. J. Math. 101 (1979), 915-955.
  • [5] V. Guillemin, S. Sternberg, Symplectic Techniques in Physics, Cambridge Univ. Press, Cambridge, 1984.
  • [6] S. Janeczko, Classification of lagrangian stars and their symplectic invariants, J. Phys. A 31 (1998), 3677-3685.
  • [7] S. Janeczko, Generating families for images of Lagrangian submanifolds and open swallowtails, Math. Proc. Cambridge Philos. Soc. 100 (1986), 91-107.
  • [8] S. Janeczko, Constrained Lagrangian submanifolds over singular constraining varieties and discriminant varieties, Ann. Inst. H. Poincaré Phys. Théor. 46 (1987), 1-26.
  • [9] J. B. Keller, Rays, waves and asymptotics, Bull. Amer. Math. Soc. 84 (1978), 727-750.
  • [10] J. Martinet, Singularities of Smooth Functions and Maps, London Math. Soc. Lecture Note Ser. 58, Cambridge Univ. Press, Cambridge, 1982.
  • [11] S. Marvizi, R. Melrose, Spectral invariants of convex planar regions, J. Differential Geom. 17 (1982), 475-502.
  • [12] M. Mikosz, On classification of the linear Lagrangian and isotropic subspaces, Demonstratio Math. 30 (1997), 437-450.
  • [13] J. Milnor, Morse Theory, Ann. of Math. Stud. 51, Princeton Univ. Press, Princeton, 1963.
  • [14] A. S. Mishchenko, V. E. Shatalov, B. Yu. Sternin, Lagrangian manifolds and the method of the canonical operator (in Russian), % Lagranzhevy mnogoobraziya i metod kanonicheskogo operatora, Moskow, Nauka, Moscow, 1978.
  • [15] R. Ranga Rao, On some explicit formulas in the theory of Weil representation, Pacific J. Math. 157 (1993), 335-371.
  • [16] F. Takens, J. White, Morse theory of double normals of immersions, Indiana Univ. Math. J. 21 (1971), 11-17.
  • [17] W. M. Tulczyjew, The Legendre transformation, Ann. Inst. H. Poincaré Sect. A 27 (1977), 101-114.
  • [18] A. Weinstein, Symplectic geometry, Bull. Amer. Math. Soc. (N.S.) 5 (1981), 1-13.
  • [19] A. Weinstein, Lectures on Symplectic Manifolds, CBMS Regional Conf. Ser. in Math. 29, Amer. Math. Soc., Providence, 1977; corrected reprint, 1979.
  • [20] 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv50z1p151bwm
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