Next Article in Journal
Influence of Conformational Entropy on the Protein Folding Rate
Previous Article in Journal
Entropy in the Present and Early Universe: New Small Parameters and Dark Energy Problem
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
View Full-Text   |   Download PDF [221 KB, uploaded 24 February 2015]   |  


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).

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

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

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here


[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert