Alpern, Steven and Prasad, V. S. (1999) Chaotic homeomorphisms of RN, lifted from torus homeomorphisms. Bulletin of the London mathematical society, 31 (5). pp. 577-580. ISSN 0024-6093
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.
|Additional Information:||© 1999 London Mathematical Society|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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