A canonical thickening of Q and the dynamics of continued fractions
classification
🧮 math.DS
math.NT
keywords
intervalsfractionsalpha-continuedcanonicalconjectureconstructcontainedcontinued
read the original abstract
We construct a countable family of open intervals contained in (0,1] whose endpoints are quadratic surds and such that their union is a full measure set. We then show that these intervals are precisely the monotonicity intervals of the entropy of alpha-continued fractions, thus proving a conjecture of Nakada and Natsui.
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