Ergodicity and weak-mixing of homogeneous extensions of measure-preserving transformations with applications to Markov shifts |
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Authors: | M S M Noorani |
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Institution: | (1) Department of Mathematics Faculty of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi, 43600 Selangor, Malaysia |
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Abstract: | Given a homogeneous extensionS of a measure-preserving transformationT, we provide necessary and sufficient conditions for the ergodicity and weak-mixing ofS in terms of functional equations. We then apply our findings to the case whenT is a Markov shift and the associated skewing function ofS depends on a finite number of coordinates. In this case, we obtain a simplification to the appropriate functional equations. |
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Keywords: | 28D05 |
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