| dc.creator | Aranzubia, Solange | |
| dc.creator | Carvajal, Rubén | |
| dc.creator | Labarca, Rafael | |
| dc.date | 2018-09-24 | |
| dc.date.accessioned | 2019-11-14T12:01:15Z | |
| dc.date.available | 2019-11-14T12:01:15Z | |
| dc.identifier | https://www.revistaproyecciones.cl/article/view/3163 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/113649 | |
| dc.description | The Lorenz Attractor has been a source for many mathematical studies. Most of them deal with lower dimensional representations of its first return map. An one dimensional scenario can be modeled by the standard two parameter family of contracting Lorenz maps. The dynamics, in this case, can be modeled by a subshift in the Lexicographical model. The Lexicographical model is the set of two symbols with the topology induced by the lexicographical metric and with the lexicographical order. These subshifts are the maximal invariant set for the shift map in some interval. For some of them, the extremes of the interval are a minimal periodic sequence and a maximal periodic sequence which is an iteration of the lower extreme (by the shift map). For some of these subshifts the topological entropy is zero. In this case the dynamics (of the respective Lorenz map) is simple.Associated to any of these subshifts (let call it Λ) we consider an extension (let call it Γ) that contains Λ which also can be constructed by using an interval whose extremes can be defined by the extremes of Λ. For these extensions we present here a computer verification of the result that compute its topological entropy. As a consequence, of our results, we can say: the longer the period of the periodic sequence is then the lower complexity in the dynamics of the extension the associated map has. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad Católica del Norte. | es-ES |
| dc.relation | https://www.revistaproyecciones.cl/article/view/3163/2930 | |
| dc.rights | Derechos de autor 2018 Proyecciones. Journal of Mathematics | es-ES |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | es-ES |
| dc.source | Proyecciones. Journal of Mathematics; Vol 37 No 3 (2018); 439-477 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 37 Núm. 3 (2018); 439-477 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.subject | Lexicographical world | en-US |
| dc.subject | Topological entropy | en-US |
| dc.subject | Maximal and minimal sequences | en-US |
| dc.subject | Shift map | en-US |
| dc.subject | Lorenz Maps | en-US |
| dc.title | A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario. | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Artículo revisado por pares | es-ES |
