2 problems

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Failure of quasi-everywhere transfer-matrix Lyapunov convergence for whole-line operators
Quasi-everywhere convergence conjecture. Quasi-everywhere convergence in the displayed limit may fail; equivalently, the actual non-Lyapunov exceptional set may have positive capac…
Conjectureopenergodic-operators spectral-theory transfer-matricesarXiv posted 2 days ago
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The conjecture that skew-shift models have no spectral gaps
A skew-shift model is an ergodic operator generated by skew-shift dynamics. Its spectrum is the set of spectral values of the operator, and a spectral gap is an open interval disjo…
Conjectureopenergodic-operators skew-shift-dynamics spectral-theoryarXiv posted 2 days ago

Failure of quasi-everywhere transfer-matrix Lyapunov convergence for whole-line operators