Discontinuity of the Lyapunov Exponent
classification
🧮 math.SP
math-phmath.MP
keywords
exponentlyapunovlimit-periodicdiscontinuitypotentialsconstructdensediscontinuities
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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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