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

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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…