Iterating maps on cellular complexes
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- by Stephen J. Willson PDF
- Trans. Amer. Math. Soc. 332 (1992), 225-240 Request permission
Abstract:
Let $K$ be a finite simplicial complex and $f:K \to K$ be a "skeletal" map. A digraph $D$ is defined whose vertices correspond to the simplexes of $K$ and whose arcs give information about the behavior of $f$ on the simplexes. For every walk in $D$ there exists a point of $K$ whose iterates under $f$ mimic the walk. Periodic walks are mimicked by a periodic point. Digraphs with uncountably many infinite walks are characterized; the corresponding maps $f$ exhibit complicated behavior.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 332 (1992), 225-240
- MSC: Primary 58F13; Secondary 05C20
- DOI: https://doi.org/10.1090/S0002-9947-1992-1049619-8
- MathSciNet review: 1049619