The Ten Martini Problem

384 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications (2012, background): “Avila and Jitomirskaya [7] further developed a quantitative Aubry duality to prove that almost localization implies almost reducibility for the dual model.”
Sharp phase transitions for the almost Mathieu operator (2015, methodology): “For the pure point part, Avila-Jitomirskaya [9] showed that if λ > e 16β 9 , then Hλ,α,θ has AL for a.”
A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies (2010, background): “x)−1 ∈ SO(2,R). We obtain the somewhat surprising Date: January 18, 2010. 1We must point out that the solution of the cohomological equation is an interesting problem in some concrete situations, see [AJ1]. 1 2 ARTUR AVILA, BASSAM FAYAD, AND RAPHAEL KRIKORIAN¨ result that conjugacy to a cocycle of r”
Schrödinger operators with dynamically defined potentials (2014, background): “Namely, for such frequencies, beside the known transition from absolutely continuous to singular continuous at λ = 1, there is another transition from singular continuous to spectrally localized at λ = e; see [16, 131, 133] for the conjecture and partial results, as well as [19] for the full result.”