Centre for Discrete and Applicable Mathematics |
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CDAM Research Report, LSE-CDAM-98-11May 1998 |
Steve Alpern
Abstract
A graph is called superhamiltonian if any permutation of its vertex set can be approximated by a cyclic one, allowing a uniform error of at most one edge. We apply the theory of superhamiltonian graphs to approximate a measure preserving homeomorphism of a compact manifold X by one with a periodic orbit which enters all the elements of any given finite open cover of X. By repeated approximation we obtain transitive or chaotic homeomorphisms.
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