A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario

Abstract: 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, ca...

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Autores principales:	Aranzubia,Solange, Carvajal,Rubén, Labarca,Rafael
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:	Lexicographical world topological entropy maximal and minimal sequences shift map Lorenz Maps.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300439
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spelling	oai:scielo:S0716-091720180003004392018-10-10A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical ScenarioAranzubia,SolangeCarvajal,RubénLabarca,Rafael Lexicographical world topological entropy maximal and minimal sequences shift map Lorenz Maps. Abstract: 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.3 20182018-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300439en10.4067/S0716-09172018000300439
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Lexicographical world topological entropy maximal and minimal sequences shift map Lorenz Maps.
spellingShingle	Lexicographical world topological entropy maximal and minimal sequences shift map Lorenz Maps. Aranzubia,Solange Carvajal,Rubén Labarca,Rafael A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario
description	Abstract: 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.
author	Aranzubia,Solange Carvajal,Rubén Labarca,Rafael
author_facet	Aranzubia,Solange Carvajal,Rubén Labarca,Rafael
author_sort	Aranzubia,Solange
title	A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario
title_short	A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario
title_full	A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario
title_fullStr	A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario
title_full_unstemmed	A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario
title_sort	computer verification for the value of the topological entropy for some special subshifts in the lexicographical scenario
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000300439
work_keys_str_mv	AT aranzubiasolange acomputerverificationforthevalueofthetopologicalentropyforsomespecialsubshiftsinthelexicographicalscenario AT carvajalruben acomputerverificationforthevalueofthetopologicalentropyforsomespecialsubshiftsinthelexicographicalscenario AT labarcarafael acomputerverificationforthevalueofthetopologicalentropyforsomespecialsubshiftsinthelexicographicalscenario AT aranzubiasolange computerverificationforthevalueofthetopologicalentropyforsomespecialsubshiftsinthelexicographicalscenario AT carvajalruben computerverificationforthevalueofthetopologicalentropyforsomespecialsubshiftsinthelexicographicalscenario AT labarcarafael computerverificationforthevalueofthetopologicalentropyforsomespecialsubshiftsinthelexicographicalscenario
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A computer verification for the value of the Topological Entropy for some special subshifts in the Lexicographical Scenario

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