David Damanik

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20202026

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math.SP2026

Pure Point Spectrum is Generic

Artur Avila, David Damanik

We consider Schrödinger operators in $ℓ^{2} (Z)$ with real-valued potentials in $ℓ^{\infty} (Z)$ and show that the generic spectral type is pure point. More speci…

math.SP2025

Dense Phenomena for Ergodic Schrödinger Operators: I. Spectrum, Integrated Density of States, and Lyapunov Exponent

Artur Avila, David Damanik

We consider Schrödinger operators in $ℓ^{2} (Z)$ whose potentials are defined via continuous sampling along the orbits of a homeomorphism on a compact metric space. We show that f…

math.SP2020

Schrödinger Operators With Potentials Generated by Hyperbolic Transformations: I. Positivity of the Lyapunov Exponent

Artur Avila, David Damanik, Zhenghe Zhang

We consider discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show…