| Abstract: |
| In a 1985 paper of Arnoux, Ornstein, and Weiss, it is shown that for any two aperiodic measure-preserving transformations
$(X, \mu, T)$ and $(Y, \nu, S)$, one can find a measurable function $p:X\rightarrow\mathbb{N}$ such that, by defining a ``speedup function`` $\overline{T}(x) = T^{p(x)}(x)$, $(X, \mu, \overline{T})$ is isomorphic to $(Y, \nu, S)$. The idea of a speedup was brought to the topological setting in a 2015 paper by Ash, where he considered minimal homeomorphisms on Cantor systems. By generalizing ideas of Giordano, Putnam, and Skau, Ash showed a relationship between when one topological system can be a speedup of another and the spaces of their invariant measures. Further work of Alvin, Ash, and Ormes then explored speedups of odometers and showed that a bounded speedup of an odometer would be a conjugate odometer.
The above results concern dynamical systems generated by a single transformation, i.e. $\mathbb{Z}$-actions. In this talk we will set up the situation for
$\mathbb{Z}^d$-actions and discuss some generalizations of the above results. |
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