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arXiv · 1004.3790

A canonical thickening of Q and the dynamics of continued fractions

Carlo Carminati·Giulio Tiozzo
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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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Carlo Carminati, Giulio Tiozzo. 2010-05-27. A canonical thickening of Q and the dynamics of continued fractions. https://arxiv.org/abs/1004.3790

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