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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 volume and are spatially periodic. Moreover, we show that in the space of volume‐preserving homeomorphisms of the n‐torus with mean rotation zero, those with chaotic lifts to Rn are dense, with respect to the uniform topology. An application is given for fixed points of 2‐dimensional torus homeomorphisms (Conley–Zehnder–Franks Theorem). 1991 Mathematics Subject Classification 54H20.