Abstract
We construct rank-one infinite measure preserving transformations satisfying each of the following dynamical properties: (1) ContinuousL ∞ spectrum, conservativek-fold cartesian products but nonergodic cartesian square; (2) ergodick-fold cartesian products; (3) nonconservative cartesian square. We show how to modify the construction of (1) to obtain type IIIλ transformations with similar properties.
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Supported in part by National Science Foundation grant DMS-9214077.
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Adams, T., Friedman, N. & Silva, C.E. Rank-one weak mixing for nonsingular transformations. Isr. J. Math. 102, 269–281 (1997). https://doi.org/10.1007/BF02773802
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DOI: https://doi.org/10.1007/BF02773802