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  • Bulletin of the London Mathematical Society, Volume 31, Issue 5
  • September 1999, pp. 577-580

CHAOTIC HOMEOMORPHISMS OF Rn, LIFTED FROM TORUS HOMEOMORPHISMS

  • STEVE ALPERN (a1) and V. S. PRASAD (a2)
  • Published online: 01 September 1999
Abstract

We establish the existence of self-homeomorphisms of Rn, n [ges ] 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).

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Bulletin of the London Mathematical Society
  • ISSN: 0024-6093
  • EISSN: 1469-2120
  • URL: /core/journals/bulletin-of-the-london-mathematical-society
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