Global Topology from an Embedding

Robert Gilmore; Christophe Letellier; Nicola Romanazzi

doi:10.1088/1751-8113/40/44/010

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arXiv · 0705.3427

Global Topology from an Embedding

Robert Gilmore·Christophe Letellier·Nicola Romanazzi

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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.

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Robert Gilmore, Christophe Letellier, Nicola Romanazzi. 2007-05-23. Global Topology from an Embedding. https://doi.org/10.1088/1751-8113/40/44/010

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