DCDS
Dynnikov and train track transition matrices of pseudo-Anosov braids
S. Öykü Yurttaş
Discrete & Continuous Dynamical Systems - A 2016, 36(1): 541-570 doi: 10.3934/dcds.2016.36.541
We compare the spectra of Dynnikov matrices with the spectra of the train track transition matrices of a given pseudo-Anosov braid on the finitely punctured disk, and show that these matrices are isospectral up to roots of unity and zeros under some particular conditions. It is shown, via examples, that Dynnikov matrices are much easier to compute than transition matrices, and so yield data that was previously inaccessible.
keywords: Dynnikov matrices Dynnikov coordinates train track transition matrices. train-tracks pseudo-Anosov braids

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