Strongly Transitive Maps on Symmetric Products
Keywords:
gap subshifts, induced hyperspace mappings, strongly transitive, symmetric productsAbstract
Let $X$ be a compact metric space and let $f: X \rightarrow X$ be a continuous map. For a positive integer $n$, let $F_n(X)$ be the hyperspace of all nonempty subsets of $X$ with at most $n$ points. Let $f_n: F_n(X) \rightarrow F_n(X)$ be the induced map defined by $f_n(A)= f(A)$. In this paper, we study the connection between some $\mathrm{d} y$ namical properties of $f$ and $f_n$. In particular, we are interested in the presence of the property of strong transitivity. Along the exposition, we study some aspects of the dynamics of gap subshifts.
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