Orbit equivalence and von Neumann algebras for expansive interval maps

C. Correia Ramos, Nuno Martins, Paulo R. Pinto and J. Sousa Ramos

Chaos, Solitons & Fractals, 2007, vol. 33, issue 1, 109-117

Abstract: We study the orbit equivalence relation Rτ for dynamical systems (I,τ) arising from piecewise linear maps τ: I→I on the interval I=[0,1]. Under regularity conditions, we prove that the crossed product von Neumann algebra L∞(I)×Rτ is the type IIIλ hyperfinite factor where λ∈]0,1] is determined by the subgroup of R+ generated by {m(τ(Ii))/m(Ii)}, with the Ii’s being the underlying partitioning intervals for τ and m the Lebesgue measure. Thus we compute the complete invariant for the orbit structures of these maps.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:33:y:2007:i:1:p:109-117

DOI: 10.1016/j.chaos.2006.09.083

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