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 ∈ ( 2 , 2 ] , s ≠ 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.