# Knobbly but nice

## TL;DR

This paper proves that for certain complex dynamical systems with Julia set equal to the entire plane, every piecewise smooth Jordan curve contains a point with a dense orbit, impacting the understanding of boundary structures.

## Contribution

It establishes a new result about the existence of dense orbit points on Jordan curves in systems with full-plane Julia sets, with implications for boundary analysis.

## Key findings

- Existence of dense orbit points on Jordan curves in specific dynamical systems
- Implications for boundary structures of nice sets in complex dynamics
- Enhances understanding of ergodic and geometric properties

## Abstract

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.