The Chaotic Properties of Increasing Gap Shifts
It is well known that locally everywhere onto, totally transitive, and topologically mixing are equivalent on shift of finite type. It turns out that this relation does not hold true on shift of infinite type. We introduce the increasing gap shift and determine its chaotic properties. The increasing...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2019/2936560 |
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| _version_ | 1849387166018306048 |
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| author | Nor Syahmina Kamarudin Malouh Baloush Syahida Che Dzul-Kifli |
| author_facet | Nor Syahmina Kamarudin Malouh Baloush Syahida Che Dzul-Kifli |
| author_sort | Nor Syahmina Kamarudin |
| collection | DOAJ |
| description | It is well known that locally everywhere onto, totally transitive, and topologically mixing are equivalent on shift of finite type. It turns out that this relation does not hold true on shift of infinite type. We introduce the increasing gap shift and determine its chaotic properties. The increasing gap shift and the sigma star shift serve as counterexamples to show the relation between the three chaos notions on shift of infinite type. |
| format | Article |
| id | doaj-art-331ce53958ee4b5c896d9f54fd647b6f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-331ce53958ee4b5c896d9f54fd647b6f2025-08-20T03:55:17ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/29365602936560The Chaotic Properties of Increasing Gap ShiftsNor Syahmina Kamarudin0Malouh Baloush1Syahida Che Dzul-Kifli2School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, MalaysiaIt is well known that locally everywhere onto, totally transitive, and topologically mixing are equivalent on shift of finite type. It turns out that this relation does not hold true on shift of infinite type. We introduce the increasing gap shift and determine its chaotic properties. The increasing gap shift and the sigma star shift serve as counterexamples to show the relation between the three chaos notions on shift of infinite type.http://dx.doi.org/10.1155/2019/2936560 |
| spellingShingle | Nor Syahmina Kamarudin Malouh Baloush Syahida Che Dzul-Kifli The Chaotic Properties of Increasing Gap Shifts International Journal of Mathematics and Mathematical Sciences |
| title | The Chaotic Properties of Increasing Gap Shifts |
| title_full | The Chaotic Properties of Increasing Gap Shifts |
| title_fullStr | The Chaotic Properties of Increasing Gap Shifts |
| title_full_unstemmed | The Chaotic Properties of Increasing Gap Shifts |
| title_short | The Chaotic Properties of Increasing Gap Shifts |
| title_sort | chaotic properties of increasing gap shifts |
| url | http://dx.doi.org/10.1155/2019/2936560 |
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