ALMOST-PERIODIC ERGODIC R(N)-HOMEOMORPHISMS

A homeomorphism of R(n) is called stationary if it is the uniform limi t of volume preserving homeomorphisms which are spatially periodic and have mean translation zero. We prove that ergodic homeomorphisms form a uniform topology dense G(delta) subset of the stationary homeomorph isms, thus establishing examples which are uniformly continuous with b ounded and almost periodic displacements. In the two-dimensional orien tation preserving case, ergodic homeomorphisms have fixed points (by B rouwer's Plane Translation Theorem). Hence so do orientation-preservin g area-preserving torus homeomorphisms with mean translation zero lift s (Conley-Zehnder-Frank Theorem). (C) 1995 Academic Press. Inc.