On the ergodic decomposition for a cocycle

• Autorzy: Jean-Pierre Conze , Albert Raugi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37A40: Nonsingular (and infinite-measure preserving) transformations
• 37A20: Orbit equivalence, cocycles, ergodic equivalence relations
• 37B20: Notions of recurrence
• 28D05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 117
• Numer: 1
• Strony: 121-156

Daty

wydano

2009

Twórcy

autor

Jean-Pierre Conze

• IRMAR, CNRS UMR 6625, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France

autor

Albert Raugi

• Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France

Identyfikatory

DOI

10.4064/cm117-1-8