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Published online: 2017-01-30
Line, spiral, denseNeil Dobbs (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