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...

Full description

Saved in:
Bibliographic Details
Main Authors: Nor Syahmina Kamarudin, Malouh Baloush, Syahida Che Dzul-Kifli
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2019/2936560
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849387166018306048
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
work_keys_str_mv AT norsyahminakamarudin thechaoticpropertiesofincreasinggapshifts
AT malouhbaloush thechaoticpropertiesofincreasinggapshifts
AT syahidachedzulkifli thechaoticpropertiesofincreasinggapshifts
AT norsyahminakamarudin chaoticpropertiesofincreasinggapshifts
AT malouhbaloush chaoticpropertiesofincreasinggapshifts
AT syahidachedzulkifli chaoticpropertiesofincreasinggapshifts