# Knobbly but nice

@article{Dobbs2021KnobblyBN,
title={Knobbly but nice},
author={N. Dobbs},
journal={Ergodic Theory and Dynamical Systems},
year={2021},
volume={41},
pages={2016 - 2022}
}
• N. Dobbs
• Published 2021
• Mathematics
• Ergodic Theory and Dynamical Systems
Our main result states that, under an exponential map whose Julia set is the whole complex plane, on each piecewise smooth Jordan curve there is a point whose orbit is dense. This has consequences for the boundaries of nice sets, used in induction methods to study ergodic and geometric properties of the dynamics.

#### References

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Nice sets and invariant densities in complex dynamics
• N. Dobbs
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
• 2010
Line, spiral, dense