Skip to main content
Log in

Mather sets for plane Hamiltonian systems

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

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. N. I. Akhiezer,The Calculus of Variations, Blaisdell Publ. Co., 1962.

  2. S. Aubry, P. Y. Le Daeron,The discrete Fraenkel-Kontorova model and its extensions I, Physica 8D, 381–422 (1983).

    Google Scholar 

  3. V. Bangert,Mather Sets for Twist Mappings and Geodesics on Tori, in: Dynamics Reported1, Wiley and Teubner, 1987.

  4. G. A. Bliss,Calculus of Variations (Carus Monograph1), 6. Aufl. 1971.

  5. C. Caratheodory,Variationsrechnung und Partielle Differentialgleichungen erster Ordnung, Teubner 1935.

  6. J. Denzler,Studium globaler Minimaler eines Variationsproblems, Diplomarbeit ETH Zürich, February 1987.

  7. D. Gilbarg and N. S. Trudinger,Elliptic Partial Differential Equations of Second Order, Springer Grundlehren224 (1977).

  8. M. Giaquinta,Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton Univ. Press; Ann. Math. Studies105.

  9. O. A. Ladyzhenskaya and N. N. Ural'tseva,Linear and Quasilinear Elliptic Equations, Acad. Press (1968).

  10. J. N. Mather,Existence of Quasiperiodic Orbits for Twist Homeomorphisms of the Annulus, Topology21 (1982), 457–467.

    Google Scholar 

  11. J. N. Mather,Destruction of invariant circles, submitted to Ergodic Theory and Dynamical Systems.

  12. MacKay, Stark,Lectures on Orbits of Minimal Action for Area Preserving Maps; preprint, University of Warwick, 1985.

  13. Ch. B. Morrey,Multiple Integrals in the Calculus of Variations, Springer Grundlehren 130, (1966).

  14. J. Moser,Monotone Twist Mappings and the Calculus of Variations, Ergodic Theory and Dynamical Systems6, 401–413 (1968).

    Google Scholar 

  15. J. Moser,Recent Developments in the Theory of Hamiltonian Systems, SIAM Reviews28, 459–485 (1986).

    Google Scholar 

  16. J. Moser,Minimal solutions of variational problems on a torus, Ann. Inst. Henri Poincaré,3, 229–272 (1986).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Denzler, J. Mather sets for plane Hamiltonian systems. Z. angew. Math. Phys. 38, 791–812 (1987). https://doi.org/10.1007/BF00945819

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00945819

Keywords

Navigation