Global Topology from an Embedding
Chaotic Dynamics
2009-11-13 v1
Abstract
An embedding of chaotic data into a suitable phase space creates a diffeomorphism of the original attractor with the reconstructed attractor. Although diffeomorphic, the original and reconstructed attractors may not be topologically equivalent. In a previous work we showed how the original and reconstructed attractors can differ when the original is three-dimensional and of genus-one type. In the present work we extend this result to three-dimensional attractors of arbitrary genus. This result describes symmetries exhibited by the Lorenz attractor and its reconstructions.
Cite
@article{arxiv.0705.3427,
title = {Global Topology from an Embedding},
author = {Robert Gilmore and Christophe Letellier and Nicola Romanazzi},
journal= {arXiv preprint arXiv:0705.3427},
year = {2009}
}