Iterating maps on cellular complexes

Stephen J. Willson
1992 Transactions of the American Mathematical Society  
Let K be a finite simplicial complex and f:K->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 / on the Simplexes. For every walk in D there exists a point of K whose iterates under / mimic the walk. Periodic walks are mimicked by a periodic point. Digraphs with uncountably many infinite walks are characterized; the corresponding maps / exhibit complicated behavior.
doi:10.1090/s0002-9947-1992-1049619-8 fatcat:jfh73fperbb7fnbd74ymfyeai4