Realizing semicomputable simplices by computable dynamical systems
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Fecha
2022-10-14
Profesor/a Guía
Facultad/escuela
Idioma
en
Título de la revista
ISSN de la revista
Título del volumen
Editor
Elsevier B.V.
Nombre de Curso
Licencia CC
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Licencia CC
https://creativecommons.org/licenses/by-nc-nd/4.0/
Resumen
We study the computability of the set of invariant measures of a computable dynamical system. It is known to be semicomputable but not computable in general, and we investigate which semicomputable simplices can be realized in this way. We prove that every semicomputable finite-dimensional simplex can be realized, and that every semicomputable finite-dimensional convex set is the projection of the set of invariant measures of a computable dynamical system. In particular, there exists a computable system having exactly two ergodic measures, none of which is computable. Moreover, all the dynamical systems that we build are minimal Cantor systems. © 2022 Elsevier B.V.
Notas
Indexación: Scopus.
Palabras clave
Bratteli-Vershik system, Computable analysis, Computable dynamical system, Semicomputable simplex
Citación
Theoretical Computer Science, Volume 933, Pages 43 - 54, 14 October 2022
DOI
10.1016/j.tcs.2022.09.001