Realizing semicomputable simplices by computable dynamical systems

dc.creatorCoronel Soto, Álvaro Daniel
dc.creatorFrank, Alexander
dc.creatorHoyrup, Mathieu
dc.creatorRojas González, Luis Cristóbal
dc.date.accessioned2023-08-29T19:27:14Z
dc.date.accessioned2023-09-14T21:26:59Z
dc.date.available2023-08-29T19:27:14Z
dc.date.available2023-09-14T21:26:59Z
dc.date.created2023-08-29T19:27:14Z
dc.date.issued2022
dc.identifier10.1016/j.tcs.2022.09.001
dc.identifier1879-2294
dc.identifier0304-3975
dc.identifierhttps://doi.org/10.1016/j.tcs.2022.09.001
dc.identifierhttps://repositorio.uc.cl/handle/11534/74550
dc.identifierWOS:000934337300003
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/8798462
dc.description.abstractWe 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. (C) 2022 Elsevier B.V. All rights reserved.
dc.languageen
dc.rightsacceso restringido
dc.subjectComputable dynamical system
dc.subjectSemicomputable simplex
dc.subjectBratteli-Vershik system
dc.subjectComputable analysis
dc.titleRealizing semicomputable simplices by computable dynamical systems
dc.typeartículo


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