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A Classification of Inverse Limit Spaces of Tent Maps with Finite Critical Orbit

In this paper we classify the inverse limit spaces of tent maps with a strictly preperiodic critical point by using the symbolic dynamics approach. More precisely, we prove that for $s, t \in (\sqrt{; ; ; 2}; ; ; , 2]$, $s \ne t$, if $T_s$ and $T_t$ are tent maps with strictly preperiodic critical points, then the corresponding inverse limit spaces $K_s$ and $K_t$ are not homeomorphic.

tent map; inverse limit; composant; folding point; folding pattern

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