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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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