PMID: 15244912Jul 13, 2004Paper

Embeddings of a strange attractor into R3

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Tsvetelin D TsankovRobert Gilmore

Abstract

The algorithm for determining a global Poincaré section is applied to a previously studied dynamical system on R2 x S1 and a one-parameter family of embeddings of the strange attractor it generates into R3. We find that the topological properties of the attractor are embedding dependent to a limited extent. These embeddings rigidly preserve mechanism, which is a simple stretch and fold. The embeddings studied show three discrete topological degrees of freedom: parity, global torsion, and braid type of the genus-one torus bounding the embedded attractor.

References

Apr 15, 1988·Physical Review A: General Physics·H G Solari, R Gilmore
Dec 1, 1993·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G B MindlinR Gilmore
Aug 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G B Mindlin, H G Solari
Jun 21, 1993·Physical Review Letters·T Ondarçuhu Pérez García C
Jul 5, 1993·Physical Review Letters·T Hall
Oct 4, 2003·Physical Review Letters·Tsvetelin D Tsankov, Robert Gilmore

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Citations

Nov 17, 2017·Australasian Physical & Engineering Sciences in Medicine·Babak Sharif, Amir Homayoun Jafari
Oct 4, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Christophe LetellierRobert Gilmore
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C LetellierR Gilmore
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Nicola RomanazziRobert Gilmore

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