Partial classification of Lorenz knots: Syllable permutations of torus knots words

• We define syllable permutations of symbolic words of Lorenz torus knots.
• We build an algorithm to construct symbolic words of satellite Lorenz knots.
• Some of the syllable permutation families of words are shown to be hyperbolic.
• Infinite families of hyperbolic Lorenz knots are generated in this way.
• The techniques used can be generalized to other families of Lorenz knots.

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston’s theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.