Centre for Discrete and Applicable Mathematics |
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CDAM Research Report, LSE-CDAM-98-10May 1998 |
Steve Alpern and V.S. Prasad
Abstract
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
Keywords: torus, lift, chaotic, homeomorphism
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