The Hopf argument

Yves Coudène

doi:10.3934/jmd.2007.1.147

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2007, Volume 1, Issue 1: 147-153. Doi: 10.3934/jmd.2007.1.147

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The Hopf argument

Yves Coudène^1,

1.
IRMAR, Université Rennes 1, Campus Beaulieu, bat.23, 35042 Rennes cedex

Received: June 30, 2006

Published: September 2006

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Abstract

Let $T$ be a measure-preserving transformation of a metric space $X$. Assume $T$ is conservative and $X$ can be covered by a countable family of open sets, each of finite measure. Then any eigenfunction is invariant with respect to the stable foliation of $T$.

Keywords:

Hopf argument,
ergodicity.

Mathematics Subject Classification: 37D10, 37A40, 37A25.

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