Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of the Induced Shift Map   In this article, we compare the dynamics of the shift map and its induced
counterpart on the hyperspace of the shift space. We show that many of the
properties of induced shift map can be easily demonstrated by appropriate
sequences of symbols. We compare the dynamics of the shift system $(\Omega,
\sigma)$ with its induced counterpart
$(\mathcal{K}(\Omega),\overline{\sigma})$, where $\mathcal{K}(\Omega)$ is the
hyperspace of all nonempty compact subsets of $\Omega$. Recently, such
comparisons have been studied a lot for general spaces. We continue the same
study in case of shift spaces, and bring out the significance of such a study
in terms of sequences.
  We compare the mixing properties, denseness of periodic points, various forms
of sensitivity and expansivity of the shift map and its induced counterpart. In
particular, we show their equivalence in case of the full shift. We also look
into the special case of subshifts of finite type, and in particular prove that
the properties of weakly mixing, mixing and sensitivity are equivalent in both
systems. And in the case of any general subshift, we show that the concept of
cofinite sensitivity is equivalent in both systems and for transitive
subshifts, cofinite sensitivity is equivalent to syndectic sensitivity. In the
process we prove that all sturmian subshifts are cofinitely sensitive.

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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat