Abstract
Lorenz knots and links have been an area of research for over thirty years. Their study combines several fields of mathematics, including topology, geometry, and dynamical systems. The introduction of the Lorenz template permitted a dimension reduction, the definition of the one-dimensional Lorenz map, and the use of symbolic dynamics to code its orbits. Meanwhile, Thurston’s geometrization theorem implies that all Lorenz knots can be classified as torus knots, satellites, or hyperbolic knots. Based on a list of hyperbolic knots presented by Birman and Kofman, we define three families of Lorenz knots, compute their hyperbolic volume using the topology and geometry software SnapPy and use the results to present conjectures concerning their hyperbolicity.
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Gomes, P., Franco, N., Silva, L. (2014). Families of Hyperbolic Lorenz Knots. In: Grácio, C., Fournier-Prunaret, D., Ueta, T., Nishio, Y. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9161-3_8
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DOI: https://doi.org/10.1007/978-1-4614-9161-3_8
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