Letellier, C. and Moroz, I. M. and Gilmore, R. (2008) A Comparison of Tests for Embeddings. Phys. Rev E, 78 .
![[img]](/style/images/fileicons/application_pdf.png)
| PDF 375Kb |
Official URL: http://link.aps.org/abstract/PRE/v78/e026203
Abstract
It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Dynamical Systems; Embeddings |
| Subjects: | D - G > Dynamical systems and ergodic theory |
| Research Groups: | Mathematical Geoscience Group Oxford Centre for Industrial and Applied Mathematics |
| ID Code: | 746 |
| Deposited By: | Irene Moroz |
| Deposited On: | 23 Oct 2008 |
| Last Modified: | 20 Jul 2009 15:06 |
Repository Staff Only: item control page
