Global Topology from an Embedding

Details Global Topology from an Embedding Global Topology from an Embedding

2007-05-23

arxiv.org/abs/0705.3427v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1088/1751-8113/40/44/010

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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