3 problems

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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 3 days ago
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No-gaps conjecture for the skew-shift Schrödinger spectrum
Let $H$ be the skew-shift Schrödinger operator … where … with $\omega$ irrational. Its spectrum is the set of energies $E\in\mathbb R$ for which $H-E$ fails to be invertible. No-ga…
Conjectureopenschrodinger-operators skew-shift-dynamics spectral-theoryarXiv posted 3 days ago
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Positivity conjecture for the skew-shift Lyapunov exponent
Lyapunov-exponent positivity conjecture. For every $\lambda>0$ and every $E\in\mathbb R$ , it holds that
Conjectureopenlyapunov-exponents schrodinger-operators skew-shift-dynamicsarXiv posted 3 days ago

The conjecture that skew-shift models have no spectral gaps