Meddaugh, JonathanBinder, KyleBaylor University.2019-05-232019-05-232019-05-062019-05-23https://hdl.handle.net/2104/10606For dynamical systems with the shadowing property, the omega-limit sets can be characterized by a condition of internal chain transitivity. In this thesis, we define four limit sets in the case of finitely-generated free group and monoid actions. We give a characterization for two of these limit sets in terms of a kind of internal transitivity under the condition that the group or monoid action has an asymptotic shadowing property.en-USBaylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.MathematicsTopological DynamicsThesis