Interactions between number theory and complex dynamical systems

动力系统在数学应用中无处不在，离散时间系统长期以来一直使用复分析工具进行研究。算术动力学是一个相对较新的领域，寻求将算术几何的强大工具应用于以前仅从复全纯角度考虑的问题，这是我们提出的研究重点。我们已经在使用算术几何方面取得了一些成功，例如，在后临界有限动力系统方面提供了新的见解。

Dynamical systems are ubiquitous in applications of mathematics, and discrete-time systems have long been studied using the tools of complex analysis. Arithmetic dynamics is a relatively new field, seeking to bring the adelic tools of arithmetic geometry to bear on problems previously considered only from the complex holomorphic perspective, and this is the focus of our proposed research. Already we have had some success in using arithmetic geometry to provide new insight on, for example, post-critically finite dynamical systems.