The Boshernitzan Condition and Simon's Subshift Conjecture

报告题目:The Boshernitzan Condition and Simon's Subshift Conjecture


报告人: David DamanikRice University教授)






摘要:Boshernitzan introduced a condition on a subshift that implies its unique ergodicity. The original motivation for this work was due to its applicability to subshifts associated with interval exchange transformations. Later Damanik and Lenz proved uniform convergence for locally constant SL(2,R)-cocycles over subshifts satisfying the Boshernitzan condition. As a consequence of this result they could show that the Schr\"odinger spectrum is of zero Lebesgue measure for all aperiodic subshifts satisfying this condition. Based on this work, Simon conjectured that the latter property should hold for all minimal aperiodic subshifts. This conjecture, however, turned out to be false as shown by Avila, Damanik, and Zhang. In this talk we describe these results and some ideas underlying their proofs.




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