%0 Journal Article
%T Distributional Chaoticity of the Minimal Subshift of Shift Operators
%A Yuanlin Chen
%A Tianxiu Lu
%A Jiazheng Zhao
%J Journal of Applied Mathematics and Physics
%P 1647-1660
%@ 2327-4379
%D 2024
%I Scientific Research Publishing
%R 10.4236/jamp.2024.125102
%X This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type &lt;i&gt;k&lt;/i&gt; (&lt;math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'&gt;
 &lt;mrow&gt;
  &lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;&amp;#x2208;&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt; &lt;mrow&gt;
   &lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mfrac&gt;
    &lt;mn&gt;1&lt;/mn&gt;
    &lt;mn&gt;2&lt;/mn&gt;
   &lt;/mfrac&gt;
   &lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt; &lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;
&lt;/math&gt;
), and &lt;math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'&gt;
 &lt;mrow&gt;
  &lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;
   &lt;mrow&gt;
    &lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;
  &lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;
&lt;/math&gt;
-distribution.
%K Shift Operators
%K Subshift
%K Distributional Chaoticity
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=133171