Spectrum of positive entropy multidimensional dynamical systems with a mixed time期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Spectrum of positive entropy multidimensional dynamical systems with a mixed time

Authors:	B. Kaminski

Affiliation:	Faculty of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Torun, Poland

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 of $G_{1}$ on a Lebesgue probability space has a countable Haar spectrum in the subspace $L^{2}_{0}(X,mu)ominus L^{2}_{0}(X,Pi(Phi),mu)$ , where denotes the Pinsker - algebra of , then every aperiodic positive entropy action of on has the same property. A positive answer to the question of J.P. Thouvenot is obtained as a corollary.

Keywords:	Countable Haar spectrum entropy Gaussian actions spectral measure spectrally natural

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