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Entropy 2010, 12(4), 953-960; doi:10.3390/e12040953

Entropy of Bounding Tori

1 Department of Chemistry, Technion - Israel Institute of Technology, Haifa 32000, Israel 2 Physics Department, Drexel University, Philadelphia, Pennsylvania 19104, USA
* Author to whom correspondence should be addressed.
Received: 27 January 2010 / Revised: 5 March 2010 / Accepted: 13 April 2010 / Published: 15 April 2010
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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).
Keywords: nonlinear dynamics; topology; branched manifold; bounding torus; entropy nonlinear dynamics; topology; branched manifold; bounding torus; entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Katriel, J.; Gilmore, R. Entropy of Bounding Tori. Entropy 2010, 12, 953-960.

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