Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T03:34:40.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Rotation intervals for a family of degree one circle maps

Published online by Cambridge University Press:  19 September 2008

Leo B. Jonker
Leo B. Jonker
Affiliation:
Department of Mathematics and Statistics, Queen's University, Kingston, Ont. K7L 3N6, Canada
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.

Let f be a C0 circle map of degree one with precisely one local minimum and one local maximum, and let [ρ−(f), ρ+(f)] be the interval of rotation numbers of f. We study the structure of the function ρ(λ) = ρ+(Rλ∘f), where Rλ is the rotation through the angle λ.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 3 , September 1988 , pp. 395 - 409
Copyright
Copyright © Cambridge University Press 1988

References

REFERENCES

[1]Alsedà, Lluís, Llibre, Jaume, Misiurewicz, Michal & Simó, Carles. Twist periodic orbits and topological entropy for continuous maps of the circle of degree one which have a fixed point. Ergod. Th. & Dynam. Sys. 5 (1985), 501–517.CrossRefGoogle Scholar
[2]Bamon, R., Malta, I. & Pacífico, M. J.. Changing rotation intervals of endomorphisms of the circle. Inventiones Mathematicae 83 (1986), 257–264.CrossRefGoogle Scholar
[3]Block, Louis, Coven, Ethan M., Jonker, Leo & Misiurewicz, Michal. Primary cycles on the circle. Trans. Amer. Math. Soc. (to appear).Google Scholar
[4]Collet, Pierre & Eckmann, Jean-Pierre. Iterated Maps on the Interval as Dynamical Systems. Birkhäuser: 1980.Google Scholar
[5]Hardy, G. H. & Wright, E. M.. An Introduction to the Theory of Numbers. Oxford: 1979.Google Scholar
[6]Ito, R.. Rotation sets are closed. Math. Proc. Camb. Phil. Soc. 89 (1981), 107–111.CrossRefGoogle Scholar
[7]Ito, R.. Note on rotation sets. Proc. A.M.S. 89 (1983), 730–732.CrossRefGoogle Scholar
[8]Misiurewicz, Michal. Periodic points of maps of degree one of a circle. Ergod. Th. & Dynam. Sys. 2 (1982), 221–227.CrossRefGoogle Scholar
[9]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of families of diffeomorphisms. IHES Publ. Math. 57 (1983), 5–71.CrossRefGoogle Scholar
[10]Singer, David. Stable orbits and bifurcations of maps of the interval. SIAM. J. Appl. Math. 35 (1978), 260–267.CrossRefGoogle Scholar