Line, spiral, dense

  • Neil Dobbs

    University College Dublin, Ireland
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Exponential of exponential of almost every line in the complex plane is dense in the plane. On the other hand, for lines through any point, for a set of angles of Hausdorff dimension one, exponential of exponential of a line with angle from that set is not dense in the plane. e third iterate of an oblique line is always dense.

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Neil Dobbs, Line, spiral, dense. Enseign. Math. 62 (2016), no. 1/2, pp. 91–107

DOI 10.4171/LEM/62-1/2-6