Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-98-11

May 1998

Superhamiltonian Graphs and Chaos

Steve Alpern


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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