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- W4308204089 abstract "Abstract An ergodic dynamical system $mathbf {X}$ is called dominant if it is isomorphic to a generic extension of itself. It was shown by Glasner et al [On some generic classes of ergodic measure preserving transformations. Trans. Moscow Math. Soc. 82 (1) (2021), 15–36] that Bernoulli systems with finite entropy are dominant. In this work, we show first that every ergodic system with positive entropy is dominant, and then that if $mathbf {X}$ has zero entropy, then it is not dominant." @default.
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- W4308204089 date "2022-11-04" @default.
- W4308204089 modified "2023-10-14" @default.
- W4308204089 title "An ergodic system is dominant exactly when it has positive entropy" @default.
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- W4308204089 doi "https://doi.org/10.1017/etds.2022.69" @default.
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