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.

中文翻译：

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有节制但很好

我们的主要结果表明，在其 Julia 集为整个复平面的指数映射下，在每条分段平滑的若尔当曲线上，都有一个轨道密集的点。这对边界的影响好的集合，用于归纳方法来研究动力学的遍历和几何特性。