Farey neighbors and hyperbolic Lorenz knots

Abstract

Based on symbolic dynamics of Lorenz maps, we prove that, pro- vided one conjecture due to Morton is true, then Lorenz knots asso- ciated to orbits of points in the renormalization intervals of Lorenz maps with reducible kneading invariant of type (X,Y) * S, where the sequences X and Y are Farey neighbors verifying some conditions, are hyperbolic.

16 pages, 4 figures. arXiv admin note: text overlap with arXiv:1407.6341