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

AbstractEntropy on nonautonomous maps {fi}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 ({fi}ı=0∞,I) contains an indecomposable subcontinuum. Under the second definition, called backwards entropy, it is shown that the inverse limit space of ({fi}ı=0∞,I) is not locally connected