On the ergodic decomposition for a cocycle

Jean-Pierre Conze, and Albert Raugi. "On the ergodic decomposition for a cocycle." Colloquium Mathematicae 117.1 (2009): 121-156. <http://eudml.org/doc/286628>.

@article{Jean2009,
abstract = {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 $τ_\{φ\}: (x,g) ↦ (τx,φ(x)g)$ and the cocycle $(φₙ)_\{n∈ℤ\}$ generated by φ. Using a characterization of the ergodic invariant measures for $τ_\{φ\}$, we give the form of the ergodic decomposition of $μ(dx)⊗m_\{G\}(dg)$ or more generally of the $τ_\{φ\}$-invariant measures $μ_\{χ\}(dx) ⊗ χ(g)m_\{G\}(dg)$, where $μ_\{χ\}(dx)$ is χ∘φ-conformal for an exponential χ on G.},
author = {Jean-Pierre Conze, Albert Raugi},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {121-156},
title = {On the ergodic decomposition for a cocycle},
url = {http://eudml.org/doc/286628},
volume = {117},
year = {2009},
}

TY - JOUR
AU - Jean-Pierre Conze
AU - Albert Raugi
TI - On the ergodic decomposition for a cocycle
JO - Colloquium Mathematicae
PY - 2009
VL - 117
IS - 1
SP - 121
EP - 156
AB - 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 $τ_{φ}: (x,g) ↦ (τx,φ(x)g)$ and the cocycle $(φₙ)_{n∈ℤ}$ generated by φ. Using a characterization of the ergodic invariant measures for $τ_{φ}$, we give the form of the ergodic decomposition of $μ(dx)⊗m_{G}(dg)$ or more generally of the $τ_{φ}$-invariant measures $μ_{χ}(dx) ⊗ χ(g)m_{G}(dg)$, where $μ_{χ}(dx)$ is χ∘φ-conformal for an exponential χ on G.
LA - eng
UR - http://eudml.org/doc/286628
ER -