Corpus ID: 131775962

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

@article{Westrick2019TopologicalCP,
  title={Topological completely positive entropy is no simpler in \$\mathbb Z^2\$-SFTs},
  author={L. Westrick},
  journal={arXiv: Dynamical Systems},
  year={2019}
}
  • L. Westrick
  • Published 2019
  • Mathematics
  • arXiv: Dynamical Systems
  • We construct Z^2-SFTs at every computable level of the hierarchy of topological completely positive entropy (TCPE), answering Barbieri and Garcia-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. 
    1 Citations

    Figures from this paper

    Conjugacy of reversible cellular automata
    • V. Salo
    • Mathematics, Computer Science
    • ArXiv
    • 2020
    • PDF

    References

    SHOWING 1-10 OF 20 REFERENCES
    Topologically completely positive entropy and zero-dimensional topologically completely positive entropy
    • 4
    • Highly Influential
    • PDF
    A characterization of topologically completely positive entropy for shifts of finite type
    • 3
    • Highly Influential
    • PDF
    A characterization of the entropies of multidimensional shifts of finite type
    • 134
    • PDF
    Entropy pair realization
    • 2
    • PDF
    Fixed-point tile sets and their applications
    • 57
    • Highly Influential
    • PDF
    A disjointness theorem involving topological entropy
    • 89
    • Highly Influential
    • PDF
    The expressiveness of quasiperiodic and minimal shifts of finite type
    • 2
    • PDF
    Undecidability and nonperiodicity for tilings of the plane
    • 621
    • PDF
    Higher Recursion Theory
    • 390