Farey neighbors and hyperbolic Lorenz knots

Paulo Gomes; Nuno Franco; Luís Silva

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arXiv · 1601.07070

Farey neighbors and hyperbolic Lorenz knots

Paulo Gomes·Nuno Franco·Luís Silva

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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.

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Paulo Gomes, Nuno Franco, Luís Silva. 2016-01-26. Farey neighbors and hyperbolic Lorenz knots. https://arxiv.org/abs/1601.07070

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