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Volume 27, Issue 4
A Simple Proof of the Chaoticity of Shift Map Under a New Definition of Chaos

Indranil Bhaumik, Binayak S. Choudhury & Basudeb Mukhopadhyay

DOI: 10.1007/s10496-011-0332-z

Anal. Theory Appl., 27 (2011), pp. 332-339.

Published online: 2011-11

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  • 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 $\sum_2$ containing transitive points in a simpler way with the help of a different metric. We also provide two examples, which support this new definition.

  • Keywords

symbol space, shift map, $\delta$-scrambled set, chaos, transitive points.

  • AMS Subject Headings

37B10, 37D45, 74H62

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-27-332, author = {Indranil Bhaumik , Binayak S. Choudhury , and Mukhopadhyay , Basudeb}, title = {A Simple Proof of the Chaoticity of Shift Map Under a New Definition of Chaos}, journal = {Analysis in Theory and Applications}, year = {2011}, volume = {27}, number = {4}, pages = {332--339}, 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 $\sum_2$ containing transitive points in a simpler way with the help of a different metric. We also provide two examples, which support this new definition.

}, issn = {1573-8175}, doi = {https://doi.org/10.1007/s10496-011-0332-z}, url = {http://global-sci.org/intro/article_detail/ata/4605.html} }
TY - JOUR T1 - A Simple Proof of the Chaoticity of Shift Map Under a New Definition of Chaos AU - Indranil Bhaumik , AU - Binayak S. Choudhury , AU - Mukhopadhyay , Basudeb JO - Analysis in Theory and Applications VL - 4 SP - 332 EP - 339 PY - 2011 DA - 2011/11 SN - 27 DO - http://doi.org/10.1007/s10496-011-0332-z UR - https://global-sci.org/intro/article_detail/ata/4605.html KW - symbol space, shift map, $\delta$-scrambled set, chaos, transitive points. AB -

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 $\sum_2$ containing transitive points in a simpler way with the help of a different metric. We also provide two examples, which support this new definition.

Indranil Bhaumik , Binayak S. Choudhury , and Mukhopadhyay , Basudeb. (2011). A Simple Proof of the Chaoticity of Shift Map Under a New Definition of Chaos. Analysis in Theory and Applications. 27 (4). 332-339. doi:10.1007/s10496-011-0332-z
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