On a strong dense periodicity property of shifts of finite type

Syahida Che Dzul-Kifli, Hassan Al-Muttairi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

There are various definitions of chaotic dynamical systems. The most utilized definition of chaos is Devaney chaos which isolates three components as being the essential features of chaos; transitivity, dense periodic points and sensitive dependence on initial conditions. In this paper, we focus on a strong dense periodicity property i.e. the set of points with prime period at least n is dense for each n. On shift of finite type over two symbols Σ2, we show that the strong dense periodicity property implies another strong chaotic notions; locally everywhere onto (also called exact) and totally transitive.

Original languageEnglish
Title of host publication22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia
PublisherAmerican Institute of Physics Inc.
Volume1682
ISBN (Electronic)9780735413290
DOIs
Publication statusPublished - 22 Oct 2015
Event22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014 - Selangor, Malaysia
Duration: 24 Nov 201426 Nov 2014

Other

Other22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014
CountryMalaysia
CitySelangor
Period24/11/1426/11/14

Fingerprint

chaos
periodic variations
shift
dynamical systems

Keywords

  • Devaney chaos
  • Locally everywhere onto
  • Shift of finite type
  • Totally transitive

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Che Dzul-Kifli, S., & Al-Muttairi, H. (2015). On a strong dense periodicity property of shifts of finite type. In 22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia (Vol. 1682). [040018] American Institute of Physics Inc.. https://doi.org/10.1063/1.4932491

On a strong dense periodicity property of shifts of finite type. / Che Dzul-Kifli, Syahida; Al-Muttairi, Hassan.

22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia. Vol. 1682 American Institute of Physics Inc., 2015. 040018.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Che Dzul-Kifli, S & Al-Muttairi, H 2015, On a strong dense periodicity property of shifts of finite type. in 22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia. vol. 1682, 040018, American Institute of Physics Inc., 22nd National Symposium on Mathematical Sciences: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia, SKSM 2014, Selangor, Malaysia, 24/11/14. https://doi.org/10.1063/1.4932491
Che Dzul-Kifli S, Al-Muttairi H. On a strong dense periodicity property of shifts of finite type. In 22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia. Vol. 1682. American Institute of Physics Inc. 2015. 040018 https://doi.org/10.1063/1.4932491
Che Dzul-Kifli, Syahida ; Al-Muttairi, Hassan. / On a strong dense periodicity property of shifts of finite type. 22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia. Vol. 1682 American Institute of Physics Inc., 2015.
@inproceedings{2b3d8496f8db400f9bc45e791484ab3d,
title = "On a strong dense periodicity property of shifts of finite type",
abstract = "There are various definitions of chaotic dynamical systems. The most utilized definition of chaos is Devaney chaos which isolates three components as being the essential features of chaos; transitivity, dense periodic points and sensitive dependence on initial conditions. In this paper, we focus on a strong dense periodicity property i.e. the set of points with prime period at least n is dense for each n. On shift of finite type over two symbols Σ2, we show that the strong dense periodicity property implies another strong chaotic notions; locally everywhere onto (also called exact) and totally transitive.",
keywords = "Devaney chaos, Locally everywhere onto, Shift of finite type, Totally transitive",
author = "{Che Dzul-Kifli}, Syahida and Hassan Al-Muttairi",
year = "2015",
month = "10",
day = "22",
doi = "10.1063/1.4932491",
language = "English",
volume = "1682",
booktitle = "22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia",
publisher = "American Institute of Physics Inc.",

}

TY - GEN

T1 - On a strong dense periodicity property of shifts of finite type

AU - Che Dzul-Kifli, Syahida

AU - Al-Muttairi, Hassan

PY - 2015/10/22

Y1 - 2015/10/22

N2 - There are various definitions of chaotic dynamical systems. The most utilized definition of chaos is Devaney chaos which isolates three components as being the essential features of chaos; transitivity, dense periodic points and sensitive dependence on initial conditions. In this paper, we focus on a strong dense periodicity property i.e. the set of points with prime period at least n is dense for each n. On shift of finite type over two symbols Σ2, we show that the strong dense periodicity property implies another strong chaotic notions; locally everywhere onto (also called exact) and totally transitive.

AB - There are various definitions of chaotic dynamical systems. The most utilized definition of chaos is Devaney chaos which isolates three components as being the essential features of chaos; transitivity, dense periodic points and sensitive dependence on initial conditions. In this paper, we focus on a strong dense periodicity property i.e. the set of points with prime period at least n is dense for each n. On shift of finite type over two symbols Σ2, we show that the strong dense periodicity property implies another strong chaotic notions; locally everywhere onto (also called exact) and totally transitive.

KW - Devaney chaos

KW - Locally everywhere onto

KW - Shift of finite type

KW - Totally transitive

UR - http://www.scopus.com/inward/record.url?scp=84984586710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984586710&partnerID=8YFLogxK

U2 - 10.1063/1.4932491

DO - 10.1063/1.4932491

M3 - Conference contribution

AN - SCOPUS:84984586710

VL - 1682

BT - 22nd National Symposium on Mathematical Sciences, SKSM 2014: Strengthening Research and Collaboration of Mathematical Sciences in Malaysia

PB - American Institute of Physics Inc.

ER -