Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-05T10:05:35.775Z Has data issue: false hasContentIssue false

Periodic points of surface homeomorphisms with zero entropy

Published online by Cambridge University Press:  19 September 2008

John Smillie
Affiliation:
Graduate Center-CUNY, 33 West 42 Street, New York, N.Y. 10036
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.

This paper deals with the question of which periods can occur as periods of periodic points of zero entropy surface homeomorphisms in a given isotopy class. We give new examples of isotopy classes for which there are non-trivial restrictions and describe how the possible periods can be computed. Certain phenomena occur only for surfaces of large genus. These results have applications to the periodic data question for Morse–Smale maps.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1983

References

REFERENCES

[1]Blanchard, P. & Franks, J.. The dynamical complexity of orientation reversing homeomorphisms of surfaces. Inventiones Math. 62 (1980), 333339.CrossRefGoogle Scholar
[2]Bowen, R. & Franks, J.. The periodic points of maps of the disk and interval. Topology. 15 (1976), 337342.CrossRefGoogle Scholar
[3]Batterson, S. & Smillie, J.. Filtrations and Periodic Data on Surfaces. Preprint.Google Scholar
[4]Epstein, D. B. A.. Curves on 2-manifolds and isotopies. Acta Math. 69 (1956), 135206.Google Scholar
[5]Fathi, A., Laudenbach, F. & Poenaru, N.. Travaux de Thurston sur les surfaces. Asmrisque 66–67 (1979).Google Scholar
[6]Handel, M.. The entropy of orientation-reversing homeomorphisms of surfaces. Topology. (To appear.)Google Scholar
[7]Jaco, W. & Shalen, P.. Surface homeomorphisms and periodicity. Topology 16 (1977), 347367.CrossRefGoogle Scholar
[8]Meeks, W.. Circles invariant under diffeomorphisms of finite order. J. Differential Geometry 14 (1979), 377383.Google Scholar
[9]Narasimhan, C.. The periodic behavior of Morse-Smale diffeomorphisms on compact surfaces. Trans. Amer. Math. Soc. 248 (1979), 145149.CrossRefGoogle Scholar
[10]Thurston, W.. On the geometry and dynamics of diffeomorphisms of surfaces. Preprint.Google Scholar