Noriaki Kawaguchi
For any continuous self-map of a compact metric space, we provide sufficient conditions under which the infinite direct product of the map is $ω$-chaotic. We also apply the result to obtain some examples of unusual $ω$-chaotic maps.
This paper contains 6 theorems, 28 equations.
Theorem 1
Given a continuous map $f\colon X\to X$, let $X^\mathbb{N}$ be the product space of infinitely many copies of $X$ and let be the map defined by: for any $u=(u_n)_{n\ge1},v=(v_n)_{n\ge1}\in X^\mathbb{N}$, $v=g(u)$ if and only if $v_n=f(u_n)$ for all $n\ge1$. If there are a closed subset $\Lambda$ of $X$ with $f(\Lambda)\subset\Lambda$, $p\in\Lambda$, and $z\in X$ such that then $g$ is $\omega$-ch
