Dynamics and Indecomposable Inverse Limit Spaces of Maps on Finite Graphs

Author

Robert Paul Roe, Missouri University of Science and TechnologyFollow

Abstract

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

inverse limit space; indecomposable continuum; periodic point; homoclinic orbit; finite tree; finite graph; chaos

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1993 Elsevier, All rights reserved.

Publication Date

01 Jan 1993