The dynamical properties of even shift space

Mohd Sabri Ismail, Syahida Che Dzul-Kifli

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

Abstract

A dynamical system is a system that evolves with time. Research in the field of dynamical system is largely focused on the nature of chaos on that system. Nowadays, there are various definitions of chaotic dynamical systems. However, the most well-known definition of chaos is Devaney chaos that states three chaotic conditions in its definition; sensitivity dependence on initial conditions, transitivity and density of periodic points. In this paper, we are investigating the presence of chaotic behavior in a discrete space, even shift. The even shift space is a space of all infinite sequences over symbols 0 and 1 such that between any two 1's there are an even number of 0's. By the end of this investigation, we prove that even shift space is not only Devaney chaos but also satisfies some other stronger chaotic conditions i.e. totally transitive, topologically mixing, blending, and locally everywhere onto.

Original languageEnglish
Title of host publicationProceedings of the 24th National Symposium on Mathematical Sciences
Subtitle of host publicationMathematical Sciences Exploration for the Universal Preservation, SKSM 2016
PublisherAmerican Institute of Physics Inc.
Volume1870
ISBN (Electronic)9780735415508
DOIs
Publication statusPublished - 7 Aug 2017
Event24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016 - Kuala Terengganu, Terengganu, Malaysia
Duration: 27 Sep 201629 Sep 2016

Other

Other24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016
CountryMalaysia
CityKuala Terengganu, Terengganu
Period27/9/1629/9/16

Fingerprint

chaos
dynamical systems
shift
sensitivity

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Ismail, M. S., & Che Dzul-Kifli, S. (2017). The dynamical properties of even shift space. In Proceedings of the 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016 (Vol. 1870). [030003] American Institute of Physics Inc.. https://doi.org/10.1063/1.4995828

The dynamical properties of even shift space. / Ismail, Mohd Sabri; Che Dzul-Kifli, Syahida.

Proceedings of the 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016. Vol. 1870 American Institute of Physics Inc., 2017. 030003.

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

Ismail, MS & Che Dzul-Kifli, S 2017, The dynamical properties of even shift space. in Proceedings of the 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016. vol. 1870, 030003, American Institute of Physics Inc., 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016, Kuala Terengganu, Terengganu, Malaysia, 27/9/16. https://doi.org/10.1063/1.4995828
Ismail MS, Che Dzul-Kifli S. The dynamical properties of even shift space. In Proceedings of the 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016. Vol. 1870. American Institute of Physics Inc. 2017. 030003 https://doi.org/10.1063/1.4995828
Ismail, Mohd Sabri ; Che Dzul-Kifli, Syahida. / The dynamical properties of even shift space. Proceedings of the 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016. Vol. 1870 American Institute of Physics Inc., 2017.
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