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We consider Schrodinger operators with dynamically defined potentials arising fromcontinuous sampling along orbits of strictly ergodic transformations. The Gap Labeling Theoremstates that the possible gaps in the spectrum can be canonically labelled by an at most countableset defined purely in terms of the dynamics. Which labels actually appear depends on the choice ofthe sampling function; the missing labels are said to correspond to collapsed gaps. Here we showthat for any collapsed gap, the sampling function may be continuously deformed so that the gapimmediately opens. As a corollary, we conclude that for generic sampling functions, all gaps areopen. The proof is based on the analysis of continuous SL.2;R/ cocycles, for which we obtaindynamical results of independent interest

Opening gaps in the spectrum of strictly ergodic Schrödinger operators