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 - <p style="text-align: justify;">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.</p>