Prime end rotation numbers of invariant separating contunua of annular homeomorphisms

Details Prime end rotation numbers of invariant separating contunua of annular homeomorphisms Prime end rotation numbers of invariant separating contunua of annular homeomorphisms

2010-12-05

arxiv.org/abs/1012.0981v1

Mathematics

Dynamical Systems

7 pages

Scientific paper

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 $X$.

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