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Topological completely positive entropy is no simpler in $\mathbb Z^2$-SFTs

· 2019 · math.DS · arXiv 1904.11444

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abstract

We construct Z^2-SFTs at every computable level of the hierarchy of topological completely positive entropy (TCPE), answering Barbieri and Garc\'{i}a-Ramos, who asked if there was one at level 3. Furthermore, we show the property of TCPE in Z^2-SFTs is coanalytic complete. Thus there is no simpler description of TCPE in Z^2-SFTs than in the general case.

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Dynamical pair assignments

math.DS · 2025-01-22 · conditional · novelty 6.0

Introduces dynamical pair assignments and proves the space of P-realizable systems is Borel if and only if the associated P-rank is bounded.

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  • Dynamical pair assignments math.DS · 2025-01-22 · conditional · none · ref 15 · internal anchor

    Introduces dynamical pair assignments and proves the space of P-realizable systems is Borel if and only if the associated P-rank is bounded.