David Damanik

activity

20042026

most citedCantor Spectrum for Schrödinger Operators with Potentials arising from Generalized Skew-shifts

38 citations · 58 across the 7 of their papers we have counts for

collaborators

8 papers

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.SP2024

Schrödinger Operators with Potentials Generated by Hyperbolic Transformations: II. Large Deviations and Anderson Localization

Artur Avila, David Damanik, Zhenghe Zhang

We consider discrete one-dimensional Schrödinger operators whose potentials are generated by Hölder continuous sampling along the orbits of a uniformly hyperbolic transformation. 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…

math.SP2013★ 14 cited

Singular Density of States Measure for Subshift and Quasi-Periodic Schrödinger Operators

Artur Avila, David Damanik, Zhenghe Zhang

Simon's subshift conjecture states that for every aperiodic minimal subshift of Verblunsky coefficients, the common essential support of the associated measures has zero Lebesgue m…

math.DS2009

Opening Gaps in the Spectrum of Strictly Ergodic Schrödinger Operators

Artur Avila, Jairo Bochi, David Damanik

We consider Schrödinger operators with dynamically defined potentials arising from continuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theorem st…

math.DS2007★ 38 cited

Cantor Spectrum for Schrödinger Operators with Potentials arising from Generalized Skew-shifts

Artur Avila, Jairo Bochi, David Damanik

We consider continuous $S L (2, R)$ -cocycles over a strictly ergodic homeomorphism which fibers over an almost periodic dynamical system (generalized skew-shifts). We prove t…

math.DS2004★ 6 cited

Generic singular continuous spectrum for ergodic Schrödinger operators

Artur Avila, David Damanik

We consider Schrödinger operators with ergodic potential $V_{ω} (n) = f (T^{n} (ω))$ , $n \in Z$ , $ω \in Ω$ , where $T : Ω \to Ω$ is a non-periodic homeomorphism. We show that for generic $f \in…