Accessible points rotate as prime ends in backward or forward time

Abstract

Let $X$ be a closed invariant subset of the half--open annulus $\mathbb{A}$ such that $\mathbb{A}\setminus X$ is homeomorphic to $\mathbb{A}$. We prove that either the rotation number of all forward semi--orbits of accessible points of $X$ are well--defined and equal to the prime end rotation number or the same is true for all backward semi--orbits of accessible points of $X$.

35 pages, 10 figures. To appear in J. Lond. Math Soc. (2)

References in corpus (1)

• Rotation intervals and entropy on attracting annular continua

Cited by in corpus (1)

• Mathers regions of instability for annulus diffeomorphisms