Skip to main content
Article thumbnail
Location of Repository

Omega-Limit Sets of Discrete Dynamical Systems

By Andrew David Barwell


Omega-limit sets are interesting and important objects in the study of discrete dynamical systems. Using a variety of methods, we present and extend existing results in this area of research. Of particular interest is the property of internal chain transitivity, and we present several characterizations of omega-limit sets in terms of this property. In so doing, we will often focus our attention on the property of pseudo-orbit tracing (shadowing), which plays a central role in many of the characterizations, and about which we prove several new results. We also make extensive use of symbolic dynamics, and prove new results relating to this method of analysis

Topics: QA Mathematics
Year: 2011
OAI identifier:

Suggested articles


  1. (2000). A characterization of the ω-limit sets of interval maps.
  2. (1998). A characterization of the ω-limit sets of planar continuous dynamical systems.
  3. (2010). A characterization of ω-limit sets in shift spaces. Ergodic Theory and Dynamical Systems, doi
  4. (2010). A characterization of ω-limit sets of piecewise monotone maps of the interval. doi
  5. (1992). Dynamics in one dimension,
  6. (2006). Large deviations for non-uniformly expanding maps.
  7. (1992). On Devaney’s definition of chaos. doi
  8. Shadowing, expansivity, chain transitivity and ω-limit sets.
  9. (1996). The space of ω-limit sets of a continuous map of the interval.
  10. The structure of ω-limit sets for continuous functions. Real Anal.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.