Positive entropy on nonautonomous interval maps and the topology of the inverse limit space

Entropy on nonautonomous maps { f i } ı = 0 ∞ of the interval is defined 2 ways. Under one definition, called forward entropy, it is shown that positive entropy implies that the inverse limit space of ( { f i } ı = 0 ∞ , I ) contains an indecomposable subcontinuum. Under the second definition, called backwards entropy, it is shown that the inverse limit space of ( { f i } ı = 0 ∞ , I ) is not locally connected.