Complete Set of Representations for Dissipative Chaotic Three-Dimensional Dynamical Systems

Authors

Daniel J. Cross, Haverford CollegeFollow

Document Type

Journal Article

Role

Author

Standard Number

1539-3755

Journal Title

Physical Review E

Volume

82

Issue

5

First Page

056211

Last Page

056216

Publication Date

2010

Abstract

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 R^k, 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.

Repository Citation

“Complete Set of Representations for Dissipative Chaotic Three-Dimensional Dynamical Systems,” D. J. Cross and R. Gilmore, Physical Review E 82, 056211 (2010).