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Please use this identifier to cite or link to this item: http://hdl.handle.net/1860/1839

Title: When are projections also embeddings?
Authors: Romanazzi, Nicola
Lefranc, Marc
Gilmore, Robert
Issue Date: Jun-2007
Publisher: American Physical Society
Citation: Physical Review E, 75(4): pp. 066214-1 - 066214-9.
Abstract: When a low-dimensional chaotic attractor is embedded in a three-dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: Parity, global torsion, and knot type. We discuss how they can change with the embedding. Finally, we show that the mechanism that is responsible for creating chaotic behavior is an invariant of all embeddings. These results apply only to chaotic attractors of genus one, which covers the majority of cases in which experimental data have been subjected to topological analysis. This means that the conclusions drawn from previous analyses, for example that the mechanism generating chaotic behavior is a Smale horseshoe mechanism, a reverse horseshoe, a gateau roulĂ©, an S-template branched manifold, etc., are not artifacts of the embedding chosen for the analysis.
URI: http://dx.doi.org/10.1103/PhysRevE.75.046201
Appears in Collections:Faculty Research and Publications (Physics)

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