Journal article
Differential embedding of the Lorenz attractor
Physical review. E, Statistical, nonlinear, and soft matter physics, v 81(6), pp 066220-066220
25 Jun 2010
PMID: 20866514
Abstract
Ideally an embedding of an N-dimensional dynamical system is N-dimensional. Ideally, an embedding of a dynamical system with symmetry is symmetric. Ideally, the symmetry of the embedding is the same as the symmetry of the original system. This ideal often cannot be achieved. Differential embeddings of the Lorenz system, which possesses a twofold rotation symmetry, are not ideal. While the differential embedding technique happens to yield an embedding of the Lorenz attractor in three dimensions, it does not yield an embedding of the entire flow. An embedding of the flow requires at least four dimensions. The four dimensional embedding produces a flow restricted to a twisted three dimensional manifold in R-4. This inversion symmetric three-manifold cannot be projected into any three dimensional Euclidean subspace without singularities.
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Details
- Title
- Differential embedding of the Lorenz attractor
- Creators
- Daniel J. Cross - Drexel UniversityR. Gilmore - Drexel University
- Publication Details
- Physical review. E, Statistical, nonlinear, and soft matter physics, v 81(6), pp 066220-066220
- Publisher
- Amer Physical Soc
- Number of pages
- 9
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]
- Web of Science ID
- WOS:000279173800002
- Scopus ID
- 2-s2.0-77953989193
- Other Identifier
- 991019167941604721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Physics, Fluids & Plasmas
- Physics, Mathematical