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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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Abstract

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 3.0).

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

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