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- W4308291801 abstract "In this paper, we first develop a notion of dominated splitting for $mathbb M(2,mathbb C)$-sequences and show it is a stable property under $|cdot |_infty$-perturbation. Then we show an energy parameter belongs to the spectrum of a Jacobi operator, possibly singular, if and only if the associated Jacobi cocycle does not admit dominated splitting. This generalizes the results obtained by the second author [Z] in the scenario of Schrodinger operators. Finally, we consider dynamically defined Jacobi operators whose base dynamics is only assumed to be topologically transitive. We show an energy parameter belongs to the spectrum of the operator defined by the base point with a dense orbit if and only if the dynamically defined Jacobi cocycle does not admit dominated splitting. This includes the original Johnson's theorem obtained by R. Johnson [J] for Schodinger operators and the main theorem obtained by C. Marx [Ma] for Jacobi operators as special cases." @default.
- W4308291801 created "2022-11-10" @default.
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- W4308291801 date "2021-05-18" @default.
- W4308291801 modified "2023-09-26" @default.
- W4308291801 title "On the Correspondence Between Domination and the Spectrum of Jacobi Operators" @default.
- W4308291801 doi "https://doi.org/10.48550/arxiv.2105.08362" @default.
- W4308291801 hasPublicationYear "2021" @default.
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