Entropy of Bounding Tori

doi:10.3390/e12040953

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

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Entropy of Bounding Tori

Jacob Katriel¹ and Robert Gilmore^2,*

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; in revised form: 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) ~ e^γ(g-1), with e^γ = 3, so that the “bounding tori entropy” is log(3).

Keywords: nonlinear dynamics; topology; branched manifold; bounding torus; entropy

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MDPI and ACS Style

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

AMA Style

Katriel J, Gilmore R. Entropy of Bounding Tori. Entropy. 2010; 12(4):953-960.

Chicago/Turabian Style

Katriel, Jacob; Gilmore, Robert. 2010. "Entropy of Bounding Tori." Entropy 12, no. 4: 953-960.

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