Skip to main content
Log in

Periodic solutions on hypersurfaces and a result by C. Viterbo

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Viterbo, C.: A Proof of the Weinstein Conjecture in ℝ2n. Preprint, September 1986

  2. Weinstein, A.: On the Hypotheses of Rabinowitz's Periodic Orbit Theorems. J. Differ. Equations33, 353–358 (1979)

    Google Scholar 

  3. Benci, V., Rabinowitz, P.: A priori bounds for periodic solutions of a class of Hamiltonian systems. Ergodic theory and Dynamical systems (to appear)

  4. Benci, V., Rabinowitz, P.: Critical point theorems for indefinite functionals. Invent. Math.52, 241–273 (1979)

    Google Scholar 

  5. Rabinowitz, P.: Periodic solutions of Hamiltonian systems. Commun. Pure Appl. Math.31, 157–184 (1978)

    Google Scholar 

  6. Weinstein, A.: Periodic orbits for convex Hamiltonian systems. Ann. Math.108, 507–518 (1978)

    Google Scholar 

  7. Hofer, H.: On strongly indefinite functionals with applications. Trans. Am. Math. Soc.275, 185–214 (1983)

    Google Scholar 

  8. Spanier, E.H.: Algebraic topology. New York: McGraw Hill 1966

    Google Scholar 

  9. Clarke, F., Ekeland, I.: Hamiltonian trajectories having prescribed minimal period. Commun. Pure Appl. Math.33, 103–116 (1980)

    Google Scholar 

  10. Ekeland, I., Lasry, J.M.: On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math.112, 283–319 (1980)

    Google Scholar 

  11. Ekeland, I., Hofer, H.: Periodic solutions with prescribed minimal period for convex autonomous Hamiltonian systems. Invent. Math.81, 155–188 (1985)

    Google Scholar 

  12. Ekeland, I.: Une théorie de Morse pour les systèmes hamiltoniens convexes. Ann. Inst. Henri Poincaré, Analyse non linéaires1 19–78 (1984)

    Google Scholar 

  13. Ekeland, I., Hofer, H.: Convex Hamiltonian energy surfaces and their periodic trajectories. Preprint September 1986

  14. Wilson, T.W.: On the minimal sets of nonsingular vectorfields. Ann. Math.84, 529–536 (1966)

    Google Scholar 

  15. Schweitzer, P.A.: Counterexamples to the Seifert conjecture and opening closed leaves of foliations. Ann. Math.100, 386–400 (1974)

    Google Scholar 

  16. Lima, E.: Orientability of smooth hypersurfaces and the Jordan-Brouwer separation theorem. Expos. Math. (in press) (1987)

  17. Benci, V., Hofer, H., Rabinowitz, P.: A remark on a priori bounds and existence for periodic solutions of Hamiltonian systems. To appear in Proc. NATO conf. Il Ciocco (1986)

  18. Rabinowitz, P.: Minimax methods in critical point theory with applications to differential equations. C.B.M.S. Regional Conf. Ser. in Math. 65 (1986)

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research partially supported by NSF Grant No DMS-8603149 and by the Stiftung Volkswagenwerk

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hofer, H., Zehnder, E. Periodic solutions on hypersurfaces and a result by C. Viterbo. Invent Math 90, 1–9 (1987). https://doi.org/10.1007/BF01389030

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01389030

Keywords

Navigation