Matches in SemOpenAlex for { <https://semopenalex.org/work/W2948194493> ?p ?o ?g. }
Showing items 1 to 92 of
92
with 100 items per page.
- W2948194493 abstract "The dynamics of symbolic systems, such as multidimensional subshifts of finite type or cellular automata, are known to be closely related to computability theory. In particular, the appropriate tools to describe and classify topological entropy for this kind of systems turned out to be of computational nature. Part of the great importance of these symbolic systems relies on the role they have played in understanding more general systems over non-symbolic spaces. The aim of this article is to investigate topological entropy from a computability point of view in this more general, not necessarily symbolic setting. In analogy to effective subshifts, we consider computable maps over effective compact sets in general metric spaces, and study the computability properties of their topological entropies. We show that even in this general setting, the entropy is always a $Sigma_2$-computable number. We then study how various dynamical and analytical constrains affect this upper bound, and prove that it can be lowered in different ways depending on the constraint considered. In particular, we obtain that all $Sigma_2$-computable numbers can already be realized within the class of surjective computable maps over ${0,1}^{mathbb{N}}$, but that this bound decreases to $Pi_{1}$(or upper)-computable numbers when restricted to expansive maps. On the other hand, if we change the geometry of the ambient space from the symbolic ${0,1}^{mathbb{N}}$ to the unit interval $[0,1]$, then we find a quite different situation -- we show that the possible entropies of computable systems over $[0,1]$ are exactly the $Sigma_{1}$(or lower)-computable numbers and that this characterization switches down to precisely the computable numbers when we restrict the class of system to the quadratic family." @default.
- W2948194493 created "2019-06-14" @default.
- W2948194493 creator A5000011331 @default.
- W2948194493 creator A5006084126 @default.
- W2948194493 creator A5009309137 @default.
- W2948194493 creator A5089936066 @default.
- W2948194493 date "2019-06-04" @default.
- W2948194493 modified "2023-10-12" @default.
- W2948194493 title "On the computability properties of topological entropy: a general approach" @default.
- W2948194493 cites W1409229416 @default.
- W2948194493 cites W1502058645 @default.
- W2948194493 cites W1525817413 @default.
- W2948194493 cites W1537935065 @default.
- W2948194493 cites W1545819195 @default.
- W2948194493 cites W179744317 @default.
- W2948194493 cites W1809268447 @default.
- W2948194493 cites W1839651582 @default.
- W2948194493 cites W1979684610 @default.
- W2948194493 cites W1981198727 @default.
- W2948194493 cites W1990125233 @default.
- W2948194493 cites W2047813281 @default.
- W2948194493 cites W2052399269 @default.
- W2948194493 cites W2065597356 @default.
- W2948194493 cites W2119169537 @default.
- W2948194493 cites W2140692608 @default.
- W2948194493 cites W2164189437 @default.
- W2948194493 cites W2192149141 @default.
- W2948194493 cites W2416593802 @default.
- W2948194493 cites W2591592378 @default.
- W2948194493 cites W2889226253 @default.
- W2948194493 cites W2963744057 @default.
- W2948194493 cites W2464753253 @default.
- W2948194493 hasPublicationYear "2019" @default.
- W2948194493 type Work @default.
- W2948194493 sameAs 2948194493 @default.
- W2948194493 citedByCount "0" @default.
- W2948194493 crossrefType "posted-content" @default.
- W2948194493 hasAuthorship W2948194493A5000011331 @default.
- W2948194493 hasAuthorship W2948194493A5006084126 @default.
- W2948194493 hasAuthorship W2948194493A5009309137 @default.
- W2948194493 hasAuthorship W2948194493A5089936066 @default.
- W2948194493 hasConcept C105932330 @default.
- W2948194493 hasConcept C118615104 @default.
- W2948194493 hasConcept C119238805 @default.
- W2948194493 hasConcept C152062344 @default.
- W2948194493 hasConcept C156382255 @default.
- W2948194493 hasConcept C16101541 @default.
- W2948194493 hasConcept C198043062 @default.
- W2948194493 hasConcept C202444582 @default.
- W2948194493 hasConcept C27318111 @default.
- W2948194493 hasConcept C2780350623 @default.
- W2948194493 hasConcept C33923547 @default.
- W2948194493 hasConcept C54271186 @default.
- W2948194493 hasConceptScore W2948194493C105932330 @default.
- W2948194493 hasConceptScore W2948194493C118615104 @default.
- W2948194493 hasConceptScore W2948194493C119238805 @default.
- W2948194493 hasConceptScore W2948194493C152062344 @default.
- W2948194493 hasConceptScore W2948194493C156382255 @default.
- W2948194493 hasConceptScore W2948194493C16101541 @default.
- W2948194493 hasConceptScore W2948194493C198043062 @default.
- W2948194493 hasConceptScore W2948194493C202444582 @default.
- W2948194493 hasConceptScore W2948194493C27318111 @default.
- W2948194493 hasConceptScore W2948194493C2780350623 @default.
- W2948194493 hasConceptScore W2948194493C33923547 @default.
- W2948194493 hasConceptScore W2948194493C54271186 @default.
- W2948194493 hasLocation W29481944931 @default.
- W2948194493 hasOpenAccess W2948194493 @default.
- W2948194493 hasPrimaryLocation W29481944931 @default.
- W2948194493 hasRelatedWork W128040422 @default.
- W2948194493 hasRelatedWork W1529663204 @default.
- W2948194493 hasRelatedWork W2005038809 @default.
- W2948194493 hasRelatedWork W2044009111 @default.
- W2948194493 hasRelatedWork W2096434655 @default.
- W2948194493 hasRelatedWork W2099912947 @default.
- W2948194493 hasRelatedWork W2115145127 @default.
- W2948194493 hasRelatedWork W2118251688 @default.
- W2948194493 hasRelatedWork W2577444373 @default.
- W2948194493 hasRelatedWork W2581021621 @default.
- W2948194493 hasRelatedWork W2611102007 @default.
- W2948194493 hasRelatedWork W2619672662 @default.
- W2948194493 hasRelatedWork W2772457912 @default.
- W2948194493 hasRelatedWork W2786737543 @default.
- W2948194493 hasRelatedWork W29121393 @default.
- W2948194493 hasRelatedWork W2947915984 @default.
- W2948194493 hasRelatedWork W2950374218 @default.
- W2948194493 hasRelatedWork W2979706303 @default.
- W2948194493 hasRelatedWork W3135906408 @default.
- W2948194493 hasRelatedWork W3173684735 @default.
- W2948194493 isParatext "false" @default.
- W2948194493 isRetracted "false" @default.
- W2948194493 magId "2948194493" @default.
- W2948194493 workType "article" @default.