A proof of Weinstein’s conjecture in 2 n

Claude Viterbo

Annales de l'I.H.P. Analyse non linéaire (1987)

  • Volume: 4, Issue: 4, page 337-356
  • ISSN: 0294-1449

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Viterbo, Claude. "A proof of Weinstein’s conjecture in $\mathbb {R}^{2n}$." Annales de l'I.H.P. Analyse non linéaire 4.4 (1987): 337-356. <http://eudml.org/doc/78135>.

@article{Viterbo1987,
author = {Viterbo, Claude},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {symplectic manifold; characteristic; existence of closed characteristics},
language = {eng},
number = {4},
pages = {337-356},
publisher = {Gauthier-Villars},
title = {A proof of Weinstein’s conjecture in $\mathbb \{R\}^\{2n\}$},
url = {http://eudml.org/doc/78135},
volume = {4},
year = {1987},
}

TY - JOUR
AU - Viterbo, Claude
TI - A proof of Weinstein’s conjecture in $\mathbb {R}^{2n}$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1987
PB - Gauthier-Villars
VL - 4
IS - 4
SP - 337
EP - 356
LA - eng
KW - symplectic manifold; characteristic; existence of closed characteristics
UR - http://eudml.org/doc/78135
ER -

References

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  1. [B1] A. Bahri, Un problème variationnel sans compacité dans la géométrie de contact, C.R. Acad. Sc. T. 299 Série I, 1984, pp. 757-760. Zbl0565.58018MR772088
  2. [B2] A. Bahri, Pseudo orbites des formes de contact, preprint. 
  3. [B-L-M-R] H. Berestycki, J.M. Lasry, G. Mancini and B. Ruf, Existence of Multiple Periodic Orbits on Starshaped Hamiltonian Surfaces, Comm. Pure and Appl. Math., Vol. 38, 1985, pp. 253-289. Zbl0569.58027MR784474
  4. [Bo] A. Borel, Seminar on Transformation Groups, Annals of Math. Studies, No. 46, Princeton University Press, New York, 1960. Zbl0091.37202MR116341
  5. [C-E] F. Clarke and I. Ekeland, Hamiltonian Trajectories Having Prescribed Minimal Period, Comm. Pure and Appl. Math., Vol. 33, 1980, pp. 103-113. Zbl0403.70016MR562546
  6. [E-T] I. Ekeland and R. Temam, Convex Analysis and Varational Problems, North Holland, 1976. Zbl0322.90046MR463994
  7. [F-R] E.R. Fadell and P.H. Rabinowitz, Generalized Cohomological Index Theories for Lie Group Action with an Application to Bifurcation Questions for Hamiltonian Systems, Invent. Math., Vol. 45, 1978, pp. 139-174. Zbl0403.57001MR478189
  8. [H-Z] H. Hofer and E. Zehnder, Periodic Solutions on Hypersurfaces and a Result by C. Viterbo, Invent. Math. (to appear). Zbl0631.58022MR906578
  9. [R] P.H. Rabinowitz, Periodic Solutions of Hamiltonian Systems, Comm. Pure and Appl. Math., Vol. 31, 1978, pp. 157-184. Zbl0358.70014MR467823
  10. [Se] H. Seifert, Periodische Bewegungen mechanischer Systeme, Math. Z., Vol. 51, 1948, pp. 197-216. Zbl0030.22103MR25693
  11. [W.1] A. Weinstein, Periodic Orbits for Convex Hamiltonian Systems, Ann. of Math., Vol. 108, 1978, pp. 507-518. Zbl0403.58001MR512430
  12. [W.2] A. Weinstein, On the hypotheses of Rabinowitz' periodic orbit theorem, Journal of Diff. Eq., Vol. 33, 1979, pp. 353-358. Zbl0388.58020MR543704

Citations in EuDML Documents

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  1. Xianling Fan, A Viterbo-Hofer-Zehnder type result for hamiltonian inclusions
  2. François Laudenbach, Trois constructions en topologie symplectique
  3. Chun-Gen Liu, Yiming Long, Hyperbolic characteristics on star-shaped hypersurfaces
  4. Alfred Künzle, Singular Hamiltonian systems and symplectic capacities
  5. Alfred Künzle, Symplectic Capacities in Manifolds
  6. H. Hofer, C. Viterbo, The Weinstein conjecture in cotangent bundles and related results
  7. Claude Viterbo, Capacités symplectiques et applications
  8. François Laudenbach, Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3
  9. Claude Viterbo, An introduction to symplectic topology

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