Almost Periodic Ergodic Rn-Homeomorphisms

✍ Scribed by S. Alpern

• Book ID: 102561441
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 387 KB
• Volume: 116
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.1995.1064

✦ Synopsis

A homeomorphism of (R^{\prime \prime}) is called stationary if it is the uniform limit of volume preserving homeomorphisms which are spatially periodic and have mean translation zero. We prove that ergodic homeomorphisms form a uniform topology dense (G_{\text {, s }}) subset of the stationary homeomorphisms, thus establishing examples which are uniformly continuous with bounded and almost periodic displacements. In the two-dimensional orientation preserving case. ergodic homeomorphisms have lixed points (by Brouwer's Plane Translation Theorem). Hence so do orientationpreserving area-preserving torus homeomorphisms with mean translation zero lifts (Conley 7ehnder Frank Theorem). " wys Academic Press. In