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January  2007, 1(1): 147-153. doi: 10.3934/jmd.2007.1.147

The Hopf argument

Yves Coudène 1,

1. 

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

Received  July 2006 Published  October 2006

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: ergodicity., Hopf argument.
Mathematics Subject Classification: 37D10, 37A40, 37A2.
Citation: Yves Coudène. The Hopf argument. Journal of Modern Dynamics, 2007, 1 (1) : 147-153. doi: 10.3934/jmd.2007.1.147
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