## A variation on Pisot–Vijayaraghavan numbers

Suppose a non-real algebraic integer $\alpha$ has, aside from itself and its complex conjugate $\bar\alpha$, all its algebraic conjugates of norm less than 1. Then the fractional parts of $\Re(\alpha^n)$ will cluster about 0, 1/2 and 1 as $n$ grows large.

Do such numbers have a name and/or a literature?

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