Vol. 85, No. 1, 1979

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Modelling expansion in real flows

Harvey Bayard Keynes and M. Sears

Vol. 85 (1979), No. 1, 111–124

We show that any real flow without fixed points is the homomorphic image of a suspension of the shift on a bisequence space and the homomorphism is one-to-one between invariant residual sets. If the original flow is one-dimensional this homomorphism is an isomorphism. We then use this model of a real flow to lift -expansiveness for any class of continuous functions from the reals into the reals fixing zero, and thus generalize the results of Bowen and Walters [2]. Various other properties of the suspension model are discussed.

Mathematical Subject Classification 2000
Primary: 54H20
Secondary: 58F25
Received: 9 February 1979
Published: 1 November 1979
Harvey Bayard Keynes
M. Sears