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MR2164599 (2006c:47036) 47B39 (37E10 39A70 47B36 47B80 47N50 81Q10)
Damanik, David; Killip, Rowan Almost everywhere positivity of the Lyapunov exponent for the doubling map. Comm. Math. Phys. 257 (2005), no. 2, 287--290.
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