A classification of inverse limit spaces of tent maps with a nonrecurrent critical point

Abstract

In this paper we prove the nonrecurrent case of the Ingram conjecture by showing that if $T_s$ and $T_t$ are two tent maps with nonrecurrent critical points then $\underleftarrow{lim}\left\{\left[0,1\right],T_s\right\}$ is homeomorphic to $\underleftarrow{lim}\left\{\left[0,1\right],T_t\right\}$ if and only if $s=t$.