Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-26T13:21:12.888Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic orbits and fixed points of a C1 orientation-preserving embedding of D2

Published online by Cambridge University Press:  24 October 2008

J. M. Gambaudo
J. M. Gambaudo
Affiliation:
I.M.P.A., 110 Est Dona Castorina, Jardin Botanico, C.E.P. 22460, Rio de Janeiro, R.J., Brasil
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove that any periodic orbit O of a C1 orientation-preserving embedding f of the 2-disc D2 is linked with a fixed point P in the sense that the corresponding periodic orbits {Φt(O)}t ≥ 0 and {Φt(P)}t ≥ 0 of any torus flow Φt suspending f are linked as knots in S3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 307 - 310
Copyright
Copyright © Cambridge Philosophical Society 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Asimov, D. and Franks, J.. Unremovable closed orbits. In Geometric Dynamics (ed. Palis, J.), Lecture Notes in Math. vol. 1007 (Springer-Verlag, 1983), pp. 22–29.CrossRefGoogle Scholar
[2]Gambaudo, J. M., van Strien, S. and Tresser, C.. The periodic structure of orientation preserving embeddings of the disk with entropy zero. Ann. Inst. H. Poincaré Phys. Théor. (to appear).Google Scholar
[3]Thurston, W. P.. On the geometry and dynamics of diffeomorphisms on surfaces. Bull. Amer. Math. Soc. 15 (1988), 417–431.CrossRefGoogle Scholar