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Abstract: We construct a countable family of open intervals contained in 0,1 whoseendpoints are quadratic surds and such that their union is a full measure set.We then show that these intervals are precisely the monotonicity intervals ofthe entropy of alpha-continued fractions, thus proving a conjecture of Nakadaand Natsui.



Author: Carlo Carminati, Giulio Tiozzo

Source: https://arxiv.org/







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