Bulletin of the London Mathematical Society



NOTES AND PAPERS

CHAOTIC HOMEOMORPHISMS OF Rn, LIFTED FROM TORUS HOMEOMORPHISMS


STEVE ALPERN a1 and V. 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

Abstract

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).

(Received June 1 1998)