Final Report Summary - QUASIPERIODIC (Dynamics of quasiperiodic type)
We made progress on several directions foreseen in the initial project, particularly the global theory of one-frequency cocycles, ergodic properties of the directional flow on translation surfaces and mixing properties of the Teichmuller flow, nature of the absolutely continuous spectrum of ergodic Schrodinger operators (Kotani-Last and Schrodinger conjectures).
We also made progress in several directions which we had not anticipated, particularly towards the Birkhoff conjecture, the dry ten martini problem, disproof of the Franks-Misiurewicz conjecture, dynamics of pseudorotations, and the construction of Feigenbaum Julia sets of positive Lebesgue measure.
We also made progress in several directions which we had not anticipated, particularly towards the Birkhoff conjecture, the dry ten martini problem, disproof of the Franks-Misiurewicz conjecture, dynamics of pseudorotations, and the construction of Feigenbaum Julia sets of positive Lebesgue measure.