Spectral gaps of almost Mathieu operators in the exponential regime.

For almost Mathieu operator (Hλ, α, θu) n = un + 1 + un−1+2λ cos 2π (θ + nα) un, the dry version of the Ten Martini Problem predicts that the spectrum Σλ,α of Hλ,α,θ has all gaps open for all λ ≠ 0 and α∈ℝ\Q. Avila and Jitomirskaya prove that Σλ,α has all gaps open for Diophantine αα and 0 < |λ| < 1. In the present paper, we show that Σλ,α has all gaps open for all α∈ℝ\Q with small λλ. [ABSTRACT FROM AUTHOR]