On local properties of compactly supported solutions of the two-coefficient dilation equation.

Morawiec, Janusz

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On the limit points of the fractional parts of powers of Pisot numbers

Artūras Dubickas (2006)

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We consider the sequence of fractional parts ${ξ α^{n}}$ , $n = 1, 2, 3, \dots$ , where $α > 1$ is a Pisot number and $ξ \in ℚ (α)$ is a positive number. We find the set of limit points of this sequence and describe all cases when it has a unique limit point. The case, where $ξ = 1$ and the unique limit point is zero, was earlier described by the author and Luca, independently.