Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T21:25:08.823Z Has data issue: false hasContentIssue false
  • English
  • Français

Birkhoff periodic orbits for twist maps with the graph intersection property

Published online by Cambridge University Press:  19 September 2008

David Bernstein
David Bernstein
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

In this paper we show that Birkhoff periodic orbits actually exist for arbitrary monotone twist maps satisfying the graph intersection property.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 4 , December 1985, pp. 531 - 537
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

[1]Aubry, S.. Theory of the Devil's staircase. In Seminar on the Riemann Problem and Complete Integrability, 1978–1979. (Ed. Chudnovsky, D. G.), Lecture Notes in Math. 925, Springer: Berlin-Heidelberg-New York.Google Scholar
[2]Birkhoff, G. D.. Proof of Poincare's geometric theorem. George David Birkhoff: Collected Mathematical Papers, vol. 1 Dover Publishing Inc: New York, 1968, p. 673.Google Scholar
[3]Carter, P.. An improvement of the Poincaré-Birkhoff fixed point theorem. Trans. Amer. Math. Soc. 269 no. 1, (1982), 285–299.Google Scholar
[4]Hall, G. R.. A topological version of a theorem of Mather on twist maps. Ergod. Th. & Dynam. Sys. 4 (1984), 585–603.CrossRefGoogle Scholar
[5]Katok, A.. Some remarks on Birkhoff and Mather twist map theorems. Ergod. Th. & Dynam. Sys. 2 (1982), 185–194.CrossRefGoogle Scholar
[6]Katok, A.. Periodic and quasi-periodic orbits for twist maps. In Dynamical Systems and Chaos, Springer Lecture Notes in Physics 179 (1983) 47–65.Google Scholar
[7]Katok, A.. More about Birkhoff periodic orbits and Mather sets for twist maps. Preprint.Google Scholar
[8]Mather, J. N.. Existence of quasi-periodic orbits for twist homeomorphisms. Topology (1982).CrossRefGoogle Scholar
[9]Moser, J.. Stable and Random Motions in Dynamical Systems. Princeton Univ. Press: Princeton, 1973.Google Scholar
[10]Rüssmann, H.. On the existence of invariant curves of twist mappings of an annulus. Preprint, 1982.CrossRefGoogle Scholar