A Simple Proof of the Chaoticity of Shift Map Under a New Definition of Chaos

A Simple Proof of the Chaoticity of Shift Map Under a New Definition of Chaos

Year:    2011

Author:    Indranil Bhaumik, Binayak S. Choudhury, Basudeb Mukhopadhyay

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

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

Analysis in Theory and Applications, Vol. 27 (2011), Iss. 4 : pp. 332–339

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

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

Author Details

Indranil Bhaumik

Binayak S. Choudhury

Basudeb Mukhopadhyay