Modelling expansion in real flows

Harvey Bayard Keynes and M. Sears

Vol. 85 (1979), No. 1, 111–124

DOI: 10.2140/pjm.1979.85.111

Abstract

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 ℱ-expansiveness for any class ℱ 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

Milestones

Received: 9 February 1979

Published: 1 November 1979