Omega-Limit Sets of Discrete Dynamical Systems

Barwell, Andrew David (2011). Omega-Limit Sets of Discrete Dynamical Systems. University of Birmingham. Ph.D.

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Abstract

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.

Type of Work:	Thesis (Doctorates > Ph.D.)
Award Type:	Doctorates > Ph.D.
Supervisor(s):	Supervisor(s) Email ORCID Good, Christopher UNSPECIFIED UNSPECIFIED Decent, Stephen P UNSPECIFIED UNSPECIFIED
Licence:
College/Faculty:	Colleges (2008 onwards) > College of Engineering & Physical Sciences
School or Department:	School of Mathematics
Funders:	None/not applicable
Subjects:	Q Science > QA Mathematics
URI:	http://etheses.bham.ac.uk/id/eprint/1476

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