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The diameter of the symplectomorphism group is infinite

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References

  • [A] Arnold, V.I.: Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluids parfaits. Ann. Inst. Fourier, Grenoble16, 319–361 (1966)

    Google Scholar 

  • [B] Banyaga, A.: Sur la structure de groupe des difféomorphismes qui préservent une forme symplectique. Comment. Math. Helv.53, 174–227 (1978)

    Google Scholar 

  • [C] Calabi, E.: On the group of automorphisms of a symplectic manifold. In: Gunning, R. (ed.) Problems in Analysis, Symposium in honor of S. Bochner, Princeton University Press, 1970, pp. 1–26

  • [ER] Eliashberg, Ya., Ratiu, T.: Note on the diameter of the group of symplectomorphisms of the ball, Travaux de Séminaire Sud-Rhodanien de Geometrie, 1989 (to appear)

  • [EM] Ebin, D., Marsden, J.: Groups of diffeomorphisms and the motion of an incompressible fluid. Ann. Math.92, 102–163 (1970)

    Google Scholar 

  • [Fa] Fathi, A.: Structure of the group of homeomorphisms preserving a good measure on a compact manifold. Ann. Sci. Ec. Norm. Super13, 45–93 (1980)

    Google Scholar 

  • [H] Hofer, H.: On the topological properties of symplectic maps. 1989 (preprint)

  • [MW] Marsden, J., Weinstein, A.: The Hamiltonian structure of the Maxwell-Vlasov equations, Physica,4D, 394–406 (1982)

    Google Scholar 

  • [McD] McDuff, D.: Symplectic diffeomorphisms and flux homomorphism. Invent. Math.77, 353–365 (1984)

    Google Scholar 

  • [Sh] Shnirelman, A.L.: On the geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Mat. Sbornik128 (170), 1, 1985, English translation, Math. USSR Sbornik56, 79–105 (1987)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, 94305-2125, Stanford, CA, USA

    Yakov Eliashberg

  2. Department of Mathematics, University of California, 95064, Santa Cruz, CA, USA

    Tudor Ratiu

Authors
  1. Yakov Eliashberg
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  2. Tudor Ratiu
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Partially supported by NSF grant DMS89-96210

Partially supported by NSF grant DMS8701318-01

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Eliashberg, Y., Ratiu, T. The diameter of the symplectomorphism group is infinite. Invent Math 103, 327–340 (1991). https://doi.org/10.1007/BF01239516

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