Families of hyperbolic Lorenz knots

Abstract

Lorenz knots and links have been an area of research for over thirty years. Their study combines several fields of Mathematics, incuding Topology, Geometry an Dynamical Systems. The introduction of the Lorenz template permitted a dimen- sion reduction, the definition of the one-dimensional Lorenz map and the use of symbolic dynamics to code its orbits. Meanwhile, Thurston’s geometrization theo- rem implies that all Lorenz knots can be classified as torus knots, satellites or hy- perbolic. 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 hiperbolicity.