On the ergodic decomposition for a cocycle

Jean-Pierre Conze; Albert Raugi

Colloquium Mathematicae, Tome 116 (2009), p. 121-156 / Harvested from The Polish Digital Mathematics Library

Résumé

Let (X,,μ,τ) be an ergodic dynamical system and φ be a measurable map from X to a locally compact second countable group G with left Haar measure $m_{G}$ . We consider the map $τ_{φ}$ defined on X × G by $τ_{φ} : (x, g) \mapsto (τ x, φ (x) g)$ and the cocycle ${(φ ₙ)}_{n \in ℤ}$ generated by φ. Using a characterization of the ergodic invariant measures for $τ_{φ}$ , we give the form of the ergodic decomposition of $μ (d x) \otimes m_{G} (d g)$ or more generally of the $τ_{φ}$ -invariant measures $μ_{χ} (d x) \otimes χ (g) m_{G} (d g)$ , where $μ_{χ} (d x)$ is χ∘φ-conformal for an exponential χ on G.

Publié le : 2009-01-01

Zbl 1177.37014

EUDML-ID : urn:eudml:doc:286628

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     title = {On the ergodic decomposition for a cocycle},
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     year = {2009},
     pages = {121-156},
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Jean-Pierre Conze; Albert Raugi. On the ergodic decomposition for a cocycle. Colloquium Mathematicae, Tome 116 (2009) pp. 121-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm117-1-8/