### Abstract

A 1-step shift of finite type over two symbols is a collection of sequences over symbols 0 and 1 with some constrains. The constrains are identified by a set of forbidden blocks which are not allowed to appear in any sequences in the space. The space is of finite type since the number of forbidden blocks is finite and it is of 1-step type since the forbidden blocks are of length of 2. The aim of this paper is to look at the chaotic behaviour of 1-step shift of finite type by considering all spaces of it type. We found that there are six different 1-step shifts of finite type which exhibits totally different dynamics behaviour. We explain the dynamics of each space and then discuss on the difference of the dynamic properties between these spaces. Two of them are chaotic in the sense of Devaney. However the two chaotic shift spaces have totally different behaviour where one of them has trivial dynamics. The other four spaces are not chaotic but, they have some interesting behaviour to be highlighted. It turns out that some of the non-chaotic shift spaces satisfy some chaotic properties.

Original language | English |
---|---|

Article number | 97733 |

Journal | Indian Journal of Science and Technology |

Volume | 9 |

Issue number | 46 |

DOIs | |

Publication status | Published - 2016 |

### Fingerprint

### Keywords

- Blending
- Devaney chaos
- Locally everywhere onto
- Mixing
- Shift of finite type

### ASJC Scopus subject areas

- General

### Cite this

**The dynamics of 1-step shifts of finite type over two symbols.** / Baloush, Malouh; Che Dzul-Kifli, Syahida.

Research output: Contribution to journal › Article

*Indian Journal of Science and Technology*, vol. 9, no. 46, 97733. https://doi.org/10.17485/ijst/2016/v9i46/97733

}

TY - JOUR

T1 - The dynamics of 1-step shifts of finite type over two symbols

AU - Baloush, Malouh

AU - Che Dzul-Kifli, Syahida

PY - 2016

Y1 - 2016

N2 - A 1-step shift of finite type over two symbols is a collection of sequences over symbols 0 and 1 with some constrains. The constrains are identified by a set of forbidden blocks which are not allowed to appear in any sequences in the space. The space is of finite type since the number of forbidden blocks is finite and it is of 1-step type since the forbidden blocks are of length of 2. The aim of this paper is to look at the chaotic behaviour of 1-step shift of finite type by considering all spaces of it type. We found that there are six different 1-step shifts of finite type which exhibits totally different dynamics behaviour. We explain the dynamics of each space and then discuss on the difference of the dynamic properties between these spaces. Two of them are chaotic in the sense of Devaney. However the two chaotic shift spaces have totally different behaviour where one of them has trivial dynamics. The other four spaces are not chaotic but, they have some interesting behaviour to be highlighted. It turns out that some of the non-chaotic shift spaces satisfy some chaotic properties.

AB - A 1-step shift of finite type over two symbols is a collection of sequences over symbols 0 and 1 with some constrains. The constrains are identified by a set of forbidden blocks which are not allowed to appear in any sequences in the space. The space is of finite type since the number of forbidden blocks is finite and it is of 1-step type since the forbidden blocks are of length of 2. The aim of this paper is to look at the chaotic behaviour of 1-step shift of finite type by considering all spaces of it type. We found that there are six different 1-step shifts of finite type which exhibits totally different dynamics behaviour. We explain the dynamics of each space and then discuss on the difference of the dynamic properties between these spaces. Two of them are chaotic in the sense of Devaney. However the two chaotic shift spaces have totally different behaviour where one of them has trivial dynamics. The other four spaces are not chaotic but, they have some interesting behaviour to be highlighted. It turns out that some of the non-chaotic shift spaces satisfy some chaotic properties.

KW - Blending

KW - Devaney chaos

KW - Locally everywhere onto

KW - Mixing

KW - Shift of finite type

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UR - http://www.scopus.com/inward/citedby.url?scp=85007566126&partnerID=8YFLogxK

U2 - 10.17485/ijst/2016/v9i46/97733

DO - 10.17485/ijst/2016/v9i46/97733

M3 - Article

VL - 9

JO - Indian Journal of Science and Technology

JF - Indian Journal of Science and Technology

SN - 0974-6846

IS - 46

M1 - 97733

ER -