Omega-Limit Sets of Discrete Dynamical Systems

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http://eprints.org/relation/isVolatileVersionOf http://etheses.bham.ac.uk/id/document/3505 http://eprints.org/relation/ispreviewThumbnailVersionOf http://etheses.bham.ac.uk/id/document/3505 http://eprints.org/relation/isVersionOf http://etheses.bham.ac.uk/id/document/3505 archive 4031 disk0/00/00/14/76 2011-04-01 09:43:10 2019-01-23 09:54:16 2011-07-19 16:36:58 thesis show 0 Barwell Andrew David Good Christopher Decent Stephen P University of Birmingham Omega-Limit Sets of Discrete Dynamical Systems unpub QA 10col_ephy 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of symbolic dynamics, and prove new results relating to this method of analysis. 2011-07 2010-08 graduation eng This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. public 162 University of Birmingham School of Mathematics d_ph na 2011-07 graduation