We consider the dynamics of complex rational maps on $\widehat{\mathbb{C}}$. We prove that, after reducing their orbits to a fixed number of positive values representing the Fubini–Study distances between finitely many initial elements of the orbit and the origin, ergodic properties of the rational map are preserved.

中文翻译：

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简化的动力系统

我们考虑复杂有理映射的动力学$\widehat{\mathbb{C}}$. 我们证明，在将它们的轨道减少到固定数量的正值后，表示轨道的有限多个初始元素与原点之间的 Fubini-Study 距离，有理图的遍历特性得以保留。