arXiv:1910.13536 Abstract | arXiv Analytics

arXiv:1910.13536 [math.DS]Abstract References Reviews Resources

Cantor Spectrum for CMV and Jacobi Matrices with Coefficients arising from Generalized Skew-Shifts

Published 2019-10-29Version 1

We consider continuous cocycles arising from CMV and Jacobi matrices. Assuming the Verblunsky and Jacobi coefficients arise from generalized skew-shifts, we prove that uniform hyperbolicity of the associated cocycles is $C^0$-dense. This implies that the associated CMV and Jacobi matrices have Cantor spectrum for a generic continuous sampling map.

Categories: math.DS, math-ph, math.MP

Keywords: jacobi matrices, cantor spectrum, generalized skew-shifts, coefficients arising, jacobi coefficients arise

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