Classification of a family of Lorenz knots with reducible symbolic sequences

Abstract

Based on symbolic dynamics of Lorenz maps, we prove that, provided one conjecture due to Morton is true, then a countable family of Lorenz knots associated to orbits of points in the renormalization intervals of Lorenz maps are hyperbolic. This countable family contains some of the hyperbolic Lorenz knots listed by J. Birman and I. Kofman.