| Abstract: |
| For a non-singular action of the integers, the author and collaborators have introduced the critical dimension, the index $\alpha$ for which $\Sigma_{k=0}^n \frac{d\mu \circ T^k}{d\mu}$ grows as $O(n^{\alpha})$. It`s an interesting invariant of metric equivalence which is related to some kind of non-singular entropy.
Recently, with my student Kieran Jarrett, we have been investigating how this works for other amenable group actions including $\mathbb{Z}^d$, the Heisenberg group and the lamplighter group. |
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