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A non-constant invariant function for certain ergodic flows

Published online by Cambridge University Press:  01 June 2008

SOL SCHWARTZMAN
SOL SCHWARTZMAN*
Affiliation:
Department of Mathematics, University of Rhode Island, Kingston, RI 02906, USA (email: schwartzman@math.uri.edu)
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Abstract

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Let U be the vector space of uniformly continuous real-valued functions on the real line $\mathbb {R}$ 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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 3 , June 2008 , pp. 1031 - 1035
Copyright
Copyright © Cambridge University Press 2008

References

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