Farey neighbors and hyperbolic Lorenz knots

Abstract

Based on symbolic dynamics of Lorenz maps, we prove that, provided one conjecture due to Morton is true, then Lorenz knots associated to orbits of points in the renormalization intervals of Lorenz maps with reducible kneading invariant of type [Formula: see text], where the sequences [Formula: see text] and [Formula: see text] are Farey neighbors verifying some conditions, are hyperbolic.