Periodic orbits of large diameter for circle maps
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- by Lluís Alsedà and Sylvie Ruette PDF
- Proc. Amer. Math. Soc. 138 (2010), 3211-3217 Request permission
Abstract:
Let $f$ be a continuous circle map and let $F$ be a lifting of $f$. In this paper we study how the existence of a large orbit for $F$ affects its set of periods. More precisely, we show that, if $F$ is of degree $d\geq 1$ and has a periodic orbit of diameter larger than 1, then $F$ has periodic points of period $n$ for all integers $n\geq 1$, and thus so has $f$. We also give examples showing that this result does not hold when the degree is nonpositive.References
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Additional Information
- Lluís Alsedà
- Affiliation: Departament de Matemàtiques, Edifici Cc, Universitat Autònoma de Barcelona, 08913 Cerdanyola del Vallès, Barcelona, Spain
- MR Author ID: 212847
- Email: alseda@mat.uab.cat
- Sylvie Ruette
- Affiliation: Laboratoire de Mathématiques, Bâtiment 425, CNRS UMR 8628, Université Paris-Sud 11, 91405 Orsay cedex, France
- Email: Sylvie.Ruette@math.u-psud.fr
- Received by editor(s): July 24, 2009
- Received by editor(s) in revised form: December 12, 2009, and December 15, 2009
- Published electronically: March 25, 2010
- Additional Notes: This work was partially supported by MEC grant number MTM2008-01486.
- Communicated by: Bryna Kra
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 3211-3217
- MSC (2010): Primary 37E10; Secondary 37E15
- DOI: https://doi.org/10.1090/S0002-9939-10-10332-3
- MathSciNet review: 2653946