### 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 language | English |
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Title of host publication | Proceedings of the 24th National Symposium on Mathematical Sciences |

Subtitle of host publication | Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016 |

Publisher | American Institute of Physics Inc. |

Volume | 1870 |

ISBN (Electronic) | 9780735415508 |

DOIs | |

Publication status | Published - 7 Aug 2017 |

Event | 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016 - Kuala Terengganu, Terengganu, Malaysia Duration: 27 Sep 2016 → 29 Sep 2016 |

### Other

Other | 24th National Symposium on Mathematical Sciences: Mathematical Sciences Exploration for the Universal Preservation, SKSM 2016 |
---|---|

Country | Malaysia |

City | Kuala Terengganu, Terengganu |

Period | 27/9/16 → 29/9/16 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - The dynamical properties of even shift space

AU - Ismail, Mohd Sabri

AU - Che Dzul-Kifli, Syahida

PY - 2017/8/7

Y1 - 2017/8/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85028359736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028359736&partnerID=8YFLogxK

U2 - 10.1063/1.4995828

DO - 10.1063/1.4995828

M3 - Conference contribution

VL - 1870

BT - Proceedings of the 24th National Symposium on Mathematical Sciences

PB - American Institute of Physics Inc.

ER -