Traslaciones de Transformaciones Tipo Boole Robustamente Transitivas
The study of the renowned Boole transformation and its different parametrizations havebeen made from the context of the ergodic theory for infinite measurements. Very littleis known about the study of these transformations from the perspective of topologicaldynamic systems (periodic points, invaria...
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| Format: | Article |
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Universidad Nacional de Chimborazo
2018-06-01
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| Series: | NOVASINERGIA |
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| Online Access: | http://novasinergia.unach.edu.ec/index.php/novasinergia/article/view/20/2 |
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| author | Bladismir Leal Guelvis Mata Davíd Ramírez |
| author_facet | Bladismir Leal Guelvis Mata Davíd Ramírez |
| author_sort | Bladismir Leal |
| collection | DOAJ |
| description | The study of the renowned Boole transformation and its different parametrizations havebeen made from the context of the ergodic theory for infinite measurements. Very littleis known about the study of these transformations from the perspective of topologicaldynamic systems (periodic points, invariant sets, transitivity, non-errant set, etc.), andmuch less is known about the stability of the dynamic phenomena found in this typeof transformation. In this work we show a geometric model of Boole transformation,which results to be transitive, that is, it has a dense orbit inR. Also, we show that atype of translation (one type of parameterization) of the geometric model of the Booletransformation has a transitive invariant Cantor set, whose periodic orbits are dense insuch a set. For this, we use the classical method to obtain dynamically defined Cantorsets. Finally, adapting methods for unbounded transformations with a discontinuity, weproved that, if B is a Boole transformation, then for eachε>0the translation Bεisrobustly transitive. |
| format | Article |
| id | doaj-art-e4188d033fda4e3091edfa675623a56c |
| institution | OA Journals |
| issn | 2631-2654 |
| language | English |
| publishDate | 2018-06-01 |
| publisher | Universidad Nacional de Chimborazo |
| record_format | Article |
| series | NOVASINERGIA |
| spelling | doaj-art-e4188d033fda4e3091edfa675623a56c2025-08-20T01:54:53ZengUniversidad Nacional de ChimborazoNOVASINERGIA2631-26542018-06-0111613Traslaciones de Transformaciones Tipo Boole Robustamente TransitivasBladismir Leal0Guelvis Mata1Davíd Ramírez2Universidad de Los Andes, VenezuelaUniversidad de Los Andes, VenezuelaUniversidad de Los Andes, VenezuelaThe study of the renowned Boole transformation and its different parametrizations havebeen made from the context of the ergodic theory for infinite measurements. Very littleis known about the study of these transformations from the perspective of topologicaldynamic systems (periodic points, invariant sets, transitivity, non-errant set, etc.), andmuch less is known about the stability of the dynamic phenomena found in this typeof transformation. In this work we show a geometric model of Boole transformation,which results to be transitive, that is, it has a dense orbit inR. Also, we show that atype of translation (one type of parameterization) of the geometric model of the Booletransformation has a transitive invariant Cantor set, whose periodic orbits are dense insuch a set. For this, we use the classical method to obtain dynamically defined Cantorsets. Finally, adapting methods for unbounded transformations with a discontinuity, weproved that, if B is a Boole transformation, then for eachε>0the translation Bεisrobustly transitive.http://novasinergia.unach.edu.ec/index.php/novasinergia/article/view/20/2Órbitas PeriódicasRobustamente TransitivoTransitividadTransformación de Boole |
| spellingShingle | Bladismir Leal Guelvis Mata Davíd Ramírez Traslaciones de Transformaciones Tipo Boole Robustamente Transitivas NOVASINERGIA Órbitas Periódicas Robustamente Transitivo Transitividad Transformación de Boole |
| title | Traslaciones de Transformaciones Tipo Boole Robustamente Transitivas |
| title_full | Traslaciones de Transformaciones Tipo Boole Robustamente Transitivas |
| title_fullStr | Traslaciones de Transformaciones Tipo Boole Robustamente Transitivas |
| title_full_unstemmed | Traslaciones de Transformaciones Tipo Boole Robustamente Transitivas |
| title_short | Traslaciones de Transformaciones Tipo Boole Robustamente Transitivas |
| title_sort | traslaciones de transformaciones tipo boole robustamente transitivas |
| topic | Órbitas Periódicas Robustamente Transitivo Transitividad Transformación de Boole |
| url | http://novasinergia.unach.edu.ec/index.php/novasinergia/article/view/20/2 |
| work_keys_str_mv | AT bladismirleal traslacionesdetransformacionestipoboolerobustamentetransitivas AT guelvismata traslacionesdetransformacionestipoboolerobustamentetransitivas AT davidramirez traslacionesdetransformacionestipoboolerobustamentetransitivas |