Talk:Takens' theorem

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I find this article confusing because of the way it talks about Hausdorff dimension and Whitney's theorem. In particular, it says:

Assume that the dynamics f has an invariant manifold A with Hausdorff dimension d_A (it could be a strange attractor). Using Whitney's embedding theorem, A can be embedded in k-dimensional Euclidean space with k > 2 d_A.

The Whitney's embedding theorem I know (and the article in Wikipedia) does not talk about Hausdorff dimension. The version of Takens theorem I had heard also does not deal with Hausdorff dimension, just plain old topological dimension. I have a feeling that this article might not be quite right--or is it some generalization I hadn't heard before?? does anyone know? Would it be better to have the usual statement of Takens' theorem here? --Experiment123 18:58, 14 March 2006 (UTC)

I wrote the article from memory while I was writing something on Takens. What I wrote down is most likely tainted by Sauer and friends (I remember wondering about the one that is in the original k > dim_H(A×A) + 1). Upon re-reading, it should be "using ideas from Whitney's theorem" and "manifold" should be set. — XaosBits 01:51, 15 March 2006 (UTC)

Cool! Looks good! --Experiment123 02:32, 15 March 2006 (UTC)

Fixed the Hausdorff dimension (that was wrong). The Sauer-Yorke-Casdagli version works only with box counting dimensions and not Hausdorff. Added the original references. I also feel that Takens' theorem should redirect here and the page should be moved to something more generic. — XaosBits 16:29, 15 March 2006 (UTC)