Abstract
Using Xu's conjugacy algorithm on the braid group B3[6,31] and the hyperbolicity criterion of 3-braid links by Futer–Kalfagianni–Purcell [14], we classify Lorenz knots of trip number 3 into torus knots and hyperbolic knots.Moreover, we provide another approach to this problem. Modulo a conjectural pseudo-Anosov criterion, we can also classify Lorenz knots of trip number 3 based upon the Dehornoy floor theory. The author believes that the second approach is promising for the hyperbolicity of more classes of Lorenz knots.
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