Embedology
 Tim Sauer,
 James A. Yorke,
 Martin Casdagli
 … show all 3 hide
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Mathematical formulations of the embedding methods commonly used for the reconstruction of attractors from data series are discussed. Embedding theorems, based on previous work by H. Whitney and F. Takens, are established for compact subsetsA of Euclidean space R^{k}. Ifn is an integer larger than twice the boxcounting dimension ofA, then almost every map fromR ^{ k } toR ^{ n }, in the sense of prevalence, is onetoone onA, and moreover is an embedding on smooth manifolds contained withinA. IfA is a chaotic attractor of a typical dynamical system, then the same is true for almost everydelaycoordinate map fromR ^{ k } toR ^{ n }. These results are extended in two other directions. Similar results are proved in the more general case of reconstructions which use moving averages of delay coordinates. Second, information is given on the selfintersection set that exists whenn is less than or equal to twice the boxcounting dimension ofA.
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 Title
 Embedology
 Journal

Journal of Statistical Physics
Volume 65, Issue 34 , pp 579616
 Cover Date
 19911101
 DOI
 10.1007/BF01053745
 Print ISSN
 00224715
 Online ISSN
 15729613
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 Embedding
 chaotic attractor
 attractor reconstruction
 probability one
 prevalence
 boxcounting dimension
 delay coordinates
 Industry Sectors
 Authors

 Tim Sauer ^{(1)}
 James A. Yorke ^{(2)}
 Martin Casdagli ^{(3)}
 Author Affiliations

 1. Department of Mathematical Sciences, George Mason University, 22030, Fairfax, Virginia
 2. Institute of Physical Science and Technology, University of Maryland, 20742, College Park, Maryland
 3. Santa Fe Institute, 87501, Santa Fe, New Mexico