A canonical thickening of Q and the dynamics of continued fractions

Details A canonical thickening of Q and the dynamics of continued fractions A canonical thickening of Q and the dynamics of continued fractions

2010-04-21

arxiv.org/abs/1004.3790v2

Mathematics

Dynamical Systems

23 pages, 2 figures

Scientific paper

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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