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When are projections also embeddings?
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|Title: ||When are projections also embeddings?|
|Authors: ||Romanazzi, Nicola|
|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 roulé, an S-template branched manifold, etc., are not artifacts of the
embedding chosen for the analysis.|
|Appears in Collections:||Faculty Research and Publications (Physics)|
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