English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Corresponding author: Hena Rani Biswas, Department of Mathematics, University of Barishal, Barishal-8200, Bangladesh. Email:biswas.hena@yahoo.com Abstract In this paper, we study some chaos related properties of the forward shift map σσ+ on the generalized one-sided symbol space ∑mm + ,mm(≥ 2) ∈ NN. We consider several notions of chaos available in the contemporary literature. In this paper, we prove that σσ+is Devaney chaotic, Auslander-Yorke’s chaotic and generically δδ −chaotic. We prove that σσ+is exact Devaney chaotic and as a consequence is mixing Devaney Chaotic and weak mixing Devaney Chaotic. We also provide examples to show that the forward shift map σσ+on ∑mm is topologically conjugate to the map on the space or equivalently conjugate to the map ffmm (xx) = mmxx( 1) on the space RR/ZZ. Finally, we give a counterexample to prove that not all topologically transitive maps are totally transitive. We also give an example of a continuous function that is topologically transitive but not chaotic.

Chaotic Features of the Forward Shift Map on the Generalized m-Symbol Space