Physical Review E
Embeddings are diffeomorphisms between some dynamical phase space and a reconstructed image. Different embeddings may or may not be equivalent under isotopy. We regard embeddings as representations of the dynamical phase space. We determine the topological labels required to distinguish inequivalent representations of three-dimensional dissipative dynamical systems when the embeddings are into Rk, k=3,4,5,…. Three representation labels are required for embeddings into R3, and only one is required in R4. In R5 there is a single “universal” representation.
“Complete Set of Representations for Dissipative Chaotic Three-Dimensional Dynamical Systems,” D. J. Cross and R. Gilmore, Physical Review E 82, 056211 (2010).