Global topology from an embedding

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. PACS number: 05.45.−a