Spectrum of positive entropy multidimensional dynamical systems with a mixed time
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- by B. Kaminski PDF
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Abstract:
It is shown that if an abelian countable group $G = G_{1}\oplus G_{2}$ is such that $G_{2}$ is a finite group and every aperiodic positive entropy action $\Phi$ of $G_{1}$ on a Lebesgue probability space $(X,\mathcal {B}, \mu )$ has a countable Haar spectrum in the subspace $L^{2}_{0}(X,\mu )\ominus L^{2}_{0}(X,\Pi (\Phi ),\mu )$, where $\Pi (\Phi )$ denotes the Pinsker $\sigma$- algebra of $\Phi$, then every aperiodic positive entropy action of $G$ on $(X, \mathcal {B}, \mu )$ has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.References
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Additional Information
- B. Kaminski
- Email: bkam@mat.uni.torun.pl
- Received by editor(s): November 3, 1994
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1533-1537
- MSC (1991): Primary 28D15; Secondary 60G15
- DOI: https://doi.org/10.1090/S0002-9939-96-03186-3
- MathSciNet review: 1307534