Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-98-10

May 1998

Chaotic Homeomorphisms of  Rn, Lifted from Torus Homeomorphisms

Steve Alpern and V.S. Prasad


We establish the existence of self homeomorphisms of  Rnn >= 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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