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Rotation intervals for a family of degree one circle maps

  • Leo B. Jonker (a1)
Abstract

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.

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Copyright
COPYRIGHT: © Cambridge University Press 1988
References
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[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.
[2]Bamon, R., Malta, I. & Pacífico, M. J.. Changing rotation intervals of endomorphisms of the circle. Inventiones Mathematicae 83 (1986), 257–264.
[3]Block, Louis, Coven, Ethan M., Jonker, Leo & Misiurewicz, Michal. Primary cycles on the circle. Trans. Amer. Math. Soc. (to appear).
[4]Collet, Pierre & Eckmann, Jean-Pierre. Iterated Maps on the Interval as Dynamical Systems. Birkhäuser: 1980.
[5]Hardy, G. H. & Wright, E. M.. An Introduction to the Theory of Numbers. Oxford: 1979.
[6]Ito, R.. Rotation sets are closed. Math. Proc. Camb. Phil. Soc. 89 (1981), 107–111.
[7]Ito, R.. Note on rotation sets. Proc. A.M.S. 89 (1983), 730–732.
[8]Misiurewicz, Michal. Periodic points of maps of degree one of a circle. Ergod. Th. & Dynam. Sys. 2 (1982), 221–227.
[9]Newhouse, S., Palis, J. & Takens, F.. Bifurcations and stability of families of diffeomorphisms. IHES Publ. Math. 57 (1983), 5–71.
[10]Singer, David. Stable orbits and bifurcations of maps of the interval. SIAM. J. Appl. Math. 35 (1978), 260–267.
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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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