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Title: Partial Classification of Lorenz Knots: Syllable Permutations of Torus Knots Words
Authors: Nuno, Franco
Luis, Silva
Pedro, Gomes
Keywords: Lorenz Knots
Hyperbolic knots
Symbolic Dynamics
Issue Date: 2015
Publisher: Elsevier
Citation: Paulo Gomes, Nuno Franco, Luís Silva, Partial classification of Lorenz knots: Syllable permutations of torus knots words, Physica D: Nonlinear Phenomena, Volume 306, 15 June 2015, Pages 16-24, ISSN 0167-2789, Keywords: Lorenz knots; Hyperbolic knots; Symbolic dynamics
Abstract: 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.
ISSN: 0167-2789
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

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