Discontinuity of the Lyapunov Exponent

Published 3 May 2010 in math.SP, math-ph, and math.MP | (1005.0181v1)

Abstract: We study discontinuity of the Lyapunov exponent. We construct a limit-periodic Schr\"odinger operator, of which the Lyapunov exponent has a positive measure set of discontinuities. We also show that the limit-periodic potentials, whose Lyapunov exponent is discontinuous, are dense in the space of limit-periodic potentials.

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