Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-98-08

May 1998

A Combinatorial Construction of Chaotic Homeomorphisms on Manifolds

Steve Alpern


We use a combinatorial idea of Peter Lax to construct, on any compact manifold, a self homeomorphism which is chaotic in the sense of Devaney. Moreover we show that such transformations are dense, with respect to the uniform topology, in the space of volume preserving homeomorphisms of the closed unit cube  Inn >= 2.  This work extends that of John Oxtoby, who in 1937 proved similar results for transitive transformations.

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