CHAOTIC HOMEOMORPHISMS OF Rn, LIFTED FROM
STEVE ALPERN a1andV. S. PRASAD a2 a1 London School of Economics and Political Science, Houghton Street, London WC2A 2AE a2 Department of Mathematics, University of Massachusetts, Lowell, MA 01854, USA
We establish the existence of self-homeomorphisms of Rn,
n [gt-or-equal, slanted] 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).