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On the ergodic decomposition for a cocycle

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Conze J.-P., Raugi A.

Colloquium Mathematicum

2009

tom 117

nr 1

121-156

Let (X,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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Conze J.-P.

1 Raugi A.

1 2009

Wyniki wyszukiwania

On the ergodic decomposition for a cocycle