The Dynamics of Continuous Maps of Finite Graphs through Inverse Limits

Marcy Barge, Beverly Diamond
1994 Transactions of the American Mathematical Society  
Suppose that f.G-fG is a continuous piecewise monotone function on a finite graph G . Then the following are equivalent: (i) f has positive topological entropy; (ii) there are disjoint intervals /, and I2 and a positive integer n with /lU/2Ç/"(/i)n/"(/2); (iii) the inverse limit space constructed by using / on G as a single bonding map contains an indecomposable subcontinuum. This result generalizes known results for the interval and circle.
doi:10.2307/2154506 fatcat:zzaw52g3ebekbmcd25qb6kzwum