Line, spiral, dense

@article{Dobbs2014LineSD,
  title={Line, spiral, dense},
  author={N. Dobbs},
  journal={arXiv: Classical Analysis and ODEs},
  year={2014},
  volume={62},
  pages={91-107}
}
  • N. Dobbs
  • Published 2014
  • Mathematics, Physics
  • arXiv: Classical Analysis and ODEs
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. 
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Knobbly but nice
  • N. Dobbs
  • Mathematics
  • Ergodic Theory and Dynamical Systems
  • 2021
Dense yet Elementary

References

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Sur la répartition des puissances modulo 1