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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universidad Nacional de Chimborazo
2018-06-01
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| Series: | NOVASINERGIA |
| Subjects: | |
| Online Access: | http://novasinergia.unach.edu.ec/index.php/novasinergia/article/view/20/2 |
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| Summary: | 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. |
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| ISSN: | 2631-2654 |