Prime end rotation numbers of invariant separating continua of annular homeomorphisms
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Abstract:
Let $f$ be a homeomorphism of the closed annulus $A$ isotopic to the identity, and let $X\subset \textrm {Int}A$ be an $f$-invariant continuum which separates $A$ into two domains, the upper domain $U_+$ and the lower domain $U_-$. Fixing a lift of $f$ to the universal cover of $A$, one defines the rotation set $\tilde \rho (X)$ of $X$ by means of the invariant probabilities on $X$, as well as the prime end rotation number $\check \rho _\pm$ of $U_\pm$. The purpose of this paper is to show that $\check \rho _\pm$ belongs to $\tilde \rho (X)$ for any separating invariant continuum $X$.References
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Additional Information
- Shigenori Matsumoto
- Affiliation: Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda, Surugadai, Chiyoda-ku, Tokyo, 101-8308 Japan
- MR Author ID: 214791
- ORCID: 0000-0002-5851-7235
- Email: matsumo@math.cst.nihon-u.ac.jp
- Received by editor(s): December 5, 2010
- Published electronically: November 2, 2011
- Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (C) No. 20540096.
- Communicated by: Yingfei Yi
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 839-845
- MSC (2010): Primary 37E30; Secondary 37E45
- DOI: https://doi.org/10.1090/S0002-9939-2011-11435-7
- MathSciNet review: 2869068