Entropy of Bounding Tori
Branched manifolds that describe strange attractors in R3 can be enclosed in, and are organized by, canonical bounding tori. Tori of genus g are labeled by a symbol sequence, or “periodic orbit”, of period g-1. We show that the number of distinct canonical bounding tori grows exponentially like N(g)...
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| Format: | Article |
| Language: | English |
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MDPI AG
2010-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/12/4/953/ |
| _version_ | 1811184464634576896 |
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| author | Jacob Katriel Robert Gilmore |
| author_facet | Jacob Katriel Robert Gilmore |
| author_sort | Jacob Katriel |
| collection | DOAJ |
| description | Branched manifolds that describe strange attractors in R3 can be enclosed in, and are organized by, canonical bounding tori. Tori of genus g are labeled by a symbol sequence, or “periodic orbit”, of period g-1. We show that the number of distinct canonical bounding tori grows exponentially like N(g) ~ eγ(g-1), with eγ = 3, so that the “bounding tori entropy” is log(3). |
| first_indexed | 2024-04-11T13:13:53Z |
| format | Article |
| id | doaj.art-a3be0471655e486ca39309f1ab29d20b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T13:13:53Z |
| publishDate | 2010-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a3be0471655e486ca39309f1ab29d20b2022-12-22T04:22:28ZengMDPI AGEntropy1099-43002010-04-0112495396010.3390/e12040953Entropy of Bounding ToriJacob KatrielRobert GilmoreBranched manifolds that describe strange attractors in R3 can be enclosed in, and are organized by, canonical bounding tori. Tori of genus g are labeled by a symbol sequence, or “periodic orbit”, of period g-1. We show that the number of distinct canonical bounding tori grows exponentially like N(g) ~ eγ(g-1), with eγ = 3, so that the “bounding tori entropy” is log(3).http://www.mdpi.com/1099-4300/12/4/953/nonlinear dynamicstopologybranched manifoldbounding torusentropy |
| spellingShingle | Jacob Katriel Robert Gilmore Entropy of Bounding Tori Entropy nonlinear dynamics topology branched manifold bounding torus entropy |
| title | Entropy of Bounding Tori |
| title_full | Entropy of Bounding Tori |
| title_fullStr | Entropy of Bounding Tori |
| title_full_unstemmed | Entropy of Bounding Tori |
| title_short | Entropy of Bounding Tori |
| title_sort | entropy of bounding tori |
| topic | nonlinear dynamics topology branched manifold bounding torus entropy |
| url | http://www.mdpi.com/1099-4300/12/4/953/ |
| work_keys_str_mv | AT jacobkatriel entropyofboundingtori AT robertgilmore entropyofboundingtori |