𝒞 0 -rigidity of characteristics in symplectic geometry

Emmanuel Opshtein

Annales scientifiques de l'École Normale Supérieure (2009)

  • Volume: 42, Issue: 5, page 857-864
  • ISSN: 0012-9593

Abstract

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The paper concerns a 𝒞 0 -rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.

How to cite

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Opshtein, Emmanuel. "$\mathcal {C}^0$-rigidity of characteristics in symplectic geometry." Annales scientifiques de l'École Normale Supérieure 42.5 (2009): 857-864. <http://eudml.org/doc/272241>.

@article{Opshtein2009,
abstract = {The paper concerns a $\mathcal \{C\}^0$-rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.},
author = {Opshtein, Emmanuel},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {symplectic geometry},
language = {eng},
number = {5},
pages = {857-864},
publisher = {Société mathématique de France},
title = {$\mathcal \{C\}^0$-rigidity of characteristics in symplectic geometry},
url = {http://eudml.org/doc/272241},
volume = {42},
year = {2009},
}

TY - JOUR
AU - Opshtein, Emmanuel
TI - $\mathcal {C}^0$-rigidity of characteristics in symplectic geometry
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2009
PB - Société mathématique de France
VL - 42
IS - 5
SP - 857
EP - 864
AB - The paper concerns a $\mathcal {C}^0$-rigidity result for the characteristic foliations in symplectic geometry. A symplectic homeomorphism (in the sense of Eliashberg-Gromov) which preserves a smooth hypersurface also preserves its characteristic foliation.
LA - eng
KW - symplectic geometry
UR - http://eudml.org/doc/272241
ER -

References

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  9. [9] H. Hofer & E. Zehnder, Symplectic invariants and Hamiltonian dynamics, Birkhäuser Advanced Texts: Basler Lehrbücher, 1994. Zbl0805.58003MR1306732
  10. [10] F. Lalonde & D. McDuff, Local non-squeezing theorems and stability, Geom. Funct. Anal.5 (1995), 364–386. Zbl0837.58014MR1334871
  11. [11] F. Laudenbach & J.-C. Sikorav, Hamiltonian disjunction and limits of Lagrangian submanifolds, Int. Math. Res. Not. 1994 (1994). Zbl0812.53031MR1266111
  12. [12] D. McDuff & D. Salamon, Introduction to symplectic topology, second éd., Oxford Mathematical Monographs, Oxford Univ. Press, 1998. Zbl0844.58029MR1698616
  13. [13] E. Opshtein, Maximal symplectic packings in ℙ 2 , Compos. Math.143 (2007), 1558–1575. Zbl1133.53057MR2371382
  14. [14] G. Paternain, L. Polterovich & K. Siburg, Boundary rigidity for Lagrangian submanifolds, non-removable intersections, and Aubry-Mather theory, Mosc. Math. J. 3 (2003), 593–619, 745. Zbl1048.53058MR2025275
  15. [15] D. Sullivan, Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math.36 (1976), 225–255. Zbl0335.57015MR433464

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