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Unremovable periodic orbits of homeomorphisms

Published online by Cambridge University Press:  24 October 2008

Toby Hall
Toby Hall
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW
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Extract

In [1], Asimov and Franks give conditions under which a collection of periodic orbits of a diffeomorphism f:M→M of a compact manifold persists under arbitrary isotopy of f. Together with the Nielsen–Thurston theory, their result has been of pivotal importance in recent work on the periodic orbit structure of surface automorphisms (for example [3, 4, 7, 8, 9, 12, 13]). However, their proof uses bifurcation theory and as such depends crucially upon the differentiability of f. The periodic orbit results which make use of the Asimov–Franks theorem are therefore applicable only in the differentiable case, a limitation which belies their topological character. In this paper we shall use classical Nielsen-theoretic methods to prove the analogue of the Asimov–Franks result for homeomorphisms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 523 - 531
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

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