a1 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy (email: firstname.lastname@example.org)
a2 Department of Mathematics, Harvard University, 1 Oxford Street, 02138 Cambridge, MA, USA (email: email@example.com)
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 α-continued fractions, thus proving a conjecture of Nakada and Natsui.
(Received May 20 2010)
(Revised May 31 2011)
(Online publication September 14 2011)