The expressiveness of quasiperiodic and minimal shifts of finite type
We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in general, without restriction. We show that some quasiperiodic shifts of finite type admit only non-computable configuratio...
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| Veröffentlicht in: | Ergodic theory and dynamical systems 2021-04, Vol.41 (4), p.1086-1138 |
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| container_title | Ergodic theory and dynamical systems |
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| creator | DURAND, BRUNO ROMASHCHENKO, ANDREI |
| description | We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in general, without restriction. We show that some quasiperiodic shifts of finite type admit only non-computable configurations; we characterize the classes of Turing degrees that can be represented by quasiperiodic shifts of finite type. We also transpose to the classes of minimal/quasiperiodic shifts of finite type some results on subdynamics previously known for effective shifts without restrictions: every effective minimal (quasiperiodic) shift of dimension
$d$
can be represented as a projection of a subdynamics of a minimal (respectively, quasiperiodic) shift of finite type of dimension
$d+1$
. |
| doi_str_mv | 10.1017/etds.2019.112 |
| format | Article |
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$d$
can be represented as a projection of a subdynamics of a minimal (respectively, quasiperiodic) shift of finite type of dimension
$d+1$
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$d$
can be represented as a projection of a subdynamics of a minimal (respectively, quasiperiodic) shift of finite type of dimension
$d+1$
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Th. Dynam. Sys</addtitle><date>2021-04-01</date><risdate>2021</risdate><volume>41</volume><issue>4</issue><spage>1086</spage><epage>1138</epage><pages>1086-1138</pages><issn>0143-3857</issn><eissn>1469-4417</eissn><abstract>We study multidimensional minimal and quasiperiodic shifts of finite type. We prove for these classes several results that were previously known for the shifts of finite type in general, without restriction. We show that some quasiperiodic shifts of finite type admit only non-computable configurations; we characterize the classes of Turing degrees that can be represented by quasiperiodic shifts of finite type. We also transpose to the classes of minimal/quasiperiodic shifts of finite type some results on subdynamics previously known for effective shifts without restrictions: every effective minimal (quasiperiodic) shift of dimension
$d$
can be represented as a projection of a subdynamics of a minimal (respectively, quasiperiodic) shift of finite type of dimension
$d+1$
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| subjects | Computer Science Discrete Mathematics Dynamical Systems Mathematics Mathematics, Applied Original Article Physical Sciences Science & Technology |
| title | The expressiveness of quasiperiodic and minimal shifts of finite type |
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