Dominated Splittings and the Spectrum for Almost Periodic Jacobi Operators
We prove that the resolvent set of any, possibly singular, quasi- periodic Jacobi operator is characterized as the set of all energies whose associated Jacobi cocycles induce a dominated splitting. This extends a well-known result by Johnson for Schrödinger operators.
Marx, Chris. December 1, 2014. "Dominated Splittings and the Spectrum for Almost Periodic Jacobi Operators." Nonlinearity 27(12): 3059-3072.
IOP Publishing with London Mathematical Society
Quasi-periodic operators, Spectral theory, Dynamical systems