## The dynamics of continuous maps of finite graphs through inverse limits

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- by Marcy Barge and Beverly Diamond PDF
- Trans. Amer. Math. Soc.
**344**(1994), 773-790 Request permission

## Abstract:

Suppose that $f:G \to G$ 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 ${I_1}$, and ${I_2}$ and a positive integer

*n*with \[ {I_1} \cup {I_2} \subseteq {f^n}({I_1}) \cap {f^n}({I_2});\] (iii) the inverse limit space constructed by using

*f*on

*G*as a single bonding map contains an indecomposable subcontinuum. This result generalizes known results for the interval and circle.

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## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**344**(1994), 773-790 - MSC: Primary 58F03; Secondary 54H20, 58F13
- DOI: https://doi.org/10.1090/S0002-9947-1994-1236222-1
- MathSciNet review: 1236222