Chaotic Homeomorphisms of Rn, Lifted from Torus Homeomorphisms

We establish the existence of self-homeomorphisms of Rⁿ, n 2, which are chaotic in the sense of Devaney, preserve volumeand are spatially periodic. Moreover, we show that in the spaceof volume-preserving homeomorphisms of the n-torus with meanrotation zero, those with chaotic lifts to Rⁿ are dense, withrespect to the uniform topology. An application is given forfixed points of 2-dimensional torus homeomorphisms (Conley–Zehnder–FranksTheorem). 1991 Mathematics Subject Classification 54H20.