| Abstract: |
| We prove that an ergodic automorphism $T$ of the torus, $\mathbb T^d$ is universal. That is: for any ergodic measure-preserving transformation, $S$, of a space $(X,\mu)$ such that $h_\mu(S)$ is smaller than the topological entropy of $T$, there exists an injective factor map $\pi\colon X\to \mathbb T^d$ (informally, the dynamical system $T$ contains a copy of $(X,\mu,S)$.
Benjy Weiss has shown how to use this to obtain as a corollary that an invariant proposed by Halmos contains less information than the rational spectrum of a transformation. |
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