Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Prime end rotation numbers of invariant separating continua of annular homeomorphisms

Author: Shigenori Matsumoto
Journal: Proc. Amer. Math. Soc. 140 (2012), 839-845
MSC (2010): Primary 37E30; Secondary 37E45
Published electronically: November 2, 2011
MathSciNet review: 2869068
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ be a homeomorphism of the closed annulus $ A$ isotopic to the identity, and let $ X\subset {\rm 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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 37E30, 37E45

Retrieve articles in all journals with MSC (2010): 37E30, 37E45

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

Keywords: Continuum, rotation set, prime end rotation number, Brouwer line, foliations
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society