Journal of Modern Dynamics (JMD)

The Hopf argument

Pages: 147 - 153, Issue 1, January 2007      doi:10.3934/jmd.2007.1.147

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Yves Coudène - IRMAR, Université Rennes 1, Campus Beaulieu, bat.23, 35042 Rennes cedex, France (email)

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.

Received: July 2006;      Available Online: October 2006.