The distribution of non-Parry Perron numbers and their conjugates

We prove that the set of Perron numbers that are not Parry numbers is dense in the interval ( 1 , ∞ ) and that the set of all Galois conjugates of such numbers is dense in the whole complex plane. While the Parry numbers themselves are known also to be dense in ( 1 , ∞ ) , their conjugates are known from work of Solomyak and others to be much more restricted: they are confined to a subset of the disc | z | < ( 1 + 5 ) / 2 . Our work is in response to a remark of Akiyama, drawing attention to our lack of knowledge about non-Parry Perron numbers and their conjugates.