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A non-constant invariant function for certain ergodic flows
Published online by Cambridge University Press: 01 June 2008
Abstract
Let U be the vector space of uniformly continuous real-valued functions on the real line and let U0 denote the subspace of U consisting of all bounded uniformly continuous functions. If X is a compact differentiable manifold and we are given a flow on X, then we associate with the flow a function F:X→H1(X,U/U0) that is invariant under the flow. We give examples for which the flow on X is ergodic but there is no λ∈H1(X,U/U0) such that F(p)=λ for almost all points p.
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- Copyright © Cambridge University Press 2008