Dynamics and Indecomposable Inverse Limit Spaces of Maps on Finite Graphs
If ƒ is a map of a finite tree T having a dense orbit, then ƒ is chaotic. Also, if ƒ has a dense orbit, or a homoclinic orbit, or a periodic point of certain prescribed period, depending on the geometry of T, then the inverse limit space, (T,ƒ), having ƒ as its sole bonding map, contains indecomposable subcontinua. Finally, if X is a finite graph and ƒ has a set of periodic points of certain prescribed periods, depending on the geometry of X, then (X,ƒ) contains indecomposable subcontinua.
R. P. Roe, "Dynamics and Indecomposable Inverse Limit Spaces of Maps on Finite Graphs," Topology and its Applications, Elsevier, Jan 1993.
The definitive version is available at https://doi.org/10.1016/0166-8641(93)90016-7
Mathematics and Statistics
Keywords and Phrases
inverse limit space; indecomposable continuum; periodic point; homoclinic orbit; finite tree; finite graph; chaos
Article - Journal
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