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Chaotic homeomorphisms of RN, lifted from torus homeomorphisms

By Steven 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

Topics: QA Mathematics
Publisher: Oxford University Press on behalf of the London Mathematical Society
Year: 1999
DOI identifier: 10.1112/S002460939800561X
OAI identifier: oai:eprints.lse.ac.uk:7635
Provided by: LSE Research Online
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