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2021•International Journal of Statistics and Applied MathematicsOpen access

Stronger chaotic features of the complemented shift map on m-symbol space

Hena Rani Biswas, Md. Shahidul Islam

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Abstract

This study aims to show that the chaoticity and related properties of the complemented shift map. In the sense of Devaney as well as generically chaotic with δ=diam(∑_m ), we verify that complemented shift map σ^c is chaotic. Few strong chaotic properties of the complemented shift map have been discussed, and it has been proved that the complemented shift map is conjugate (topologically) to the shift map. Finally, we provide an example to show that σ^c is chaotic, and for that reason, we say that σ^c is an alternative chaotic model in m-symbol space.

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What this paper is about

This study aims to show that the chaoticity and related properties of the complemented shift map. In the sense of Devaney as well as generically chaotic with δ=diam(∑_m ), we verify that complemented shift map σ^c is chaotic. Few strong chaotic properties of the complemented shift map have been discussed, and it has been proved that the complemented shift map is conjugate (topologically) to the shift map. Finally, we provide an example to show that σ^c is chaotic, and for that reason, we say that σ^c is an alternative chaotic model in m-symbol space.

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Available abstract

This study aims to show that the chaoticity and related properties of the complemented shift map. In the sense of Devaney as well as generically chaotic with δ=diam(∑_m ), we verify that complemented shift map σ^c is chaotic. Few strong chaotic properties of the complemented shift map have been discussed, and it has been proved that the complemented shift map is conjugate (topologically) to the shift map. Finally, we provide an example to show that σ^c is chaotic, and for that reason, we say that σ^c is an alternative chaotic model in m-symbol space.

Key concepts: Chaotic, Chaotic map, Mathematics, Space (punctuation), Topological conjugacy, Symbol (formal), Pure mathematics, Statistical physics

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