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Badly ordered orbits of circle maps

Published online by Cambridge University Press:  24 October 2008

R. S. Mackay
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL LA 190, Pare Valrose, 06034 Nice Cedex, France
C. Tresser
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL LA 190, Pare Valrose, 06034 Nice Cedex, France

Extract

We define two notions of order for periodic orbits of circle maps, and describe some of the consequences of possession of a badly ordered periodic orbit.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Aubry, S. and Le Daeron, P. Y.. The discrete Frenkel-Kontorova model and its extensions. Phys. D 8 (1983), 381422Google Scholar
[2]Block, L., Guckenheimer, J., Misiubewicz, M. and Young, L. S.. Periodic points and Topological Entropy of One Dimensional Maps, Springer Lecture Notes in Mathematics, vol. 819 (1980)Google Scholar
[3]Bowen, R. and Franks, J.. The periodic points of maps of the disk and the interval. Topology 15 (1976), 337342CrossRefGoogle Scholar
[4]Llibbe, J.. Minimal periodic orbits of continuous mappings of the circle, Proc. Amer. Math. Soc. 83 (1981), 625628CrossRefGoogle Scholar
[5]MacKay, R. S. and Tbesseb, C.. Transition to topological chaos for circle maps, IHES preprint, to appear.Google Scholar
[6]Mather, J. N.. A criterion for the non-existence of invariant circles, preprint (Princeton,(1982), submitted to Publ. Math. IHES.Google Scholar