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Prime end rotation numbers of invariant separating contunua of annular homeomorphisms
| Content Provider | Semantic Scholar |
|---|---|
| Author | Matsumoto, Shigenori |
| Copyright Year | 2010 |
| 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 $X$. |
| Starting Page | 839 |
| Ending Page | 845 |
| Page Count | 7 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-2011-11435-7 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1012.0981v1.pdf |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/2012-140-03/S0002-9939-2011-11435-7/S0002-9939-2011-11435-7.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-2011-11435-7 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
