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L’Enseignement Mathématique

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Volume 62, Issue 1/2, 2016, pp. 91–107
DOI: 10.4171/LEM/62-1/2-6

Published online: 2017-01-30

Line, spiral, dense

Neil Dobbs[1]

(1) University College Dublin, Ireland

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.

Keywords: Elementary, dense curve, analytic curve

Dobbs Neil: Line, spiral, dense. Enseign. Math. 62 (2016), 91-107. doi: 10.4171/LEM/62-1/2-6