TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPS
Aim this article to provide an accessible introduction to the notion of topological entropy and (for context) its measure theoretic analogue, and then to present some work applying related ideas to the structure of iterated preimages for a continuous (in general non-invertible) map of a compact metr...
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| Format: | Article |
| Language: | English |
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University of Anbar
2012-06-01
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| Series: | مجلة جامعة الانبار للعلوم الصرفة |
| Subjects: | |
| Online Access: | https://juaps.uoanbar.edu.iq/article_15314_cb2356eb91d1d6482a2b5c6f50abd3df.pdf |
| _version_ | 1797373399698243584 |
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| author | Alaa A.Awad |
| author_facet | Alaa A.Awad |
| author_sort | Alaa A.Awad |
| collection | DOAJ |
| description | Aim this article to provide an accessible introduction to the notion of topological entropy and (for context) its measure theoretic analogue, and then to present some work applying related ideas to the structure of iterated preimages for a continuous (in general non-invertible) map of a compact metric space to itself. These ideas will be illustrated by tow classes of examples, form circle maps and symbolic dynamics. My focus is on motivating and explaining definitions. Most results are stated with at most a sketch of the proof. The informed reader will recognize imagery from Bowen’s exposition of topological entropy which I have freely adopted for motivation. |
| first_indexed | 2024-03-08T18:50:04Z |
| format | Article |
| id | doaj.art-7cfac0d646a64214a028ecc899ab02cb |
| institution | Directory Open Access Journal |
| issn | 1991-8941 2706-6703 |
| language | English |
| last_indexed | 2024-03-08T18:50:04Z |
| publishDate | 2012-06-01 |
| publisher | University of Anbar |
| record_format | Article |
| series | مجلة جامعة الانبار للعلوم الصرفة |
| spelling | doaj.art-7cfac0d646a64214a028ecc899ab02cb2023-12-28T21:52:41ZengUniversity of Anbarمجلة جامعة الانبار للعلوم الصرفة1991-89412706-67032012-06-01228810610.37652/juaps.2008.1531415314TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPSAlaa A.Awad0Education College / Anbar UniversityAim this article to provide an accessible introduction to the notion of topological entropy and (for context) its measure theoretic analogue, and then to present some work applying related ideas to the structure of iterated preimages for a continuous (in general non-invertible) map of a compact metric space to itself. These ideas will be illustrated by tow classes of examples, form circle maps and symbolic dynamics. My focus is on motivating and explaining definitions. Most results are stated with at most a sketch of the proof. The informed reader will recognize imagery from Bowen’s exposition of topological entropy which I have freely adopted for motivation.https://juaps.uoanbar.edu.iq/article_15314_cb2356eb91d1d6482a2b5c6f50abd3df.pdftopological entropypreimage structuremaps |
| spellingShingle | Alaa A.Awad TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPS مجلة جامعة الانبار للعلوم الصرفة topological entropy preimage structure maps |
| title | TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPS |
| title_full | TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPS |
| title_fullStr | TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPS |
| title_full_unstemmed | TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPS |
| title_short | TOPOLOGICAL ENTROPY AND THE PREIMAGE STRUCTURE OF MAPS |
| title_sort | topological entropy and the preimage structure of maps |
| topic | topological entropy preimage structure maps |
| url | https://juaps.uoanbar.edu.iq/article_15314_cb2356eb91d1d6482a2b5c6f50abd3df.pdf |
| work_keys_str_mv | AT alaaaawad topologicalentropyandthepreimagestructureofmaps |