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A simple proof of the chaoticity of shift map under a new definition of chaos

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Analysis in Theory and Applications

Abstract

Recently, Du has given a new strong definition of chaos by using the shift map. In this paper, we give a proof of the main theorem by constructing a dense uncountable invariant subset of the symbol space Σ2 containing transitive points in a simpler way with the help of a different metric. We also provide two examples, which support this new definition.

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Authors and Affiliations

  1. Bengal Engineering and Science University, SHibpur Howrah, India

    Indranil Bhaumik, Binayak S. Choudhury & Basudeb Mukhopadhyay

  2. Department of Mathematics, Bengal Engineering and Science University, SHibpur Howrah, 711103, West Bengal, India

    Indranil Bhaumik

Authors
  1. Indranil Bhaumik
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  2. Binayak S. Choudhury
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  3. Basudeb Mukhopadhyay
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Bhaumik, I., Choudhury, B.S. & Mukhopadhyay, B. A simple proof of the chaoticity of shift map under a new definition of chaos. Anal. Theory Appl. 27, 332–339 (2011). https://doi.org/10.1007/s10496-011-0332-z

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  • DOI: https://doi.org/10.1007/s10496-011-0332-z

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