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Transactions of the American Mathematical Society

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Iterating maps on cellular complexes


Author: Stephen J. Willson
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1049619-8
Keywords: Simplicial complex, digraph, chaotic dynamics
Article copyright: © Copyright 1992 American Mathematical Society

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