O-minimal Structures and their Applications to Dynamical Systems, Complex analysis and Potential Theory

在这个项目中，我们想研究o最小结构及其在动力系统、复杂分析和势理论中的应用。极小结构推广了代数型几何。分析中的重要概念和功能可以在这样的结构中实现。从公理上讲，它们具有优异的驯服性和有限性，可以应用于分析问题。公理化的表述是用数理逻辑的语言进行的。极小结构在数学基础研究中对于理解几何、逻辑和分析之间的联系非常重要。在本项目中，o-极小结构将应用于以下分析领域：a)动力系统：围绕希尔伯特第16问题的问题，第2部分；b)复分析：黎曼映射定理；c)势理论：狄利克雷问题。因此，这些研究领域之间产生了有趣的关系。

In this project we want to investigate o-minimal structures and their applications to dynamical systems, complex analysis and potential theory.O-minimal structures generalize geometries of algebraic type. Important concepts and functions from analysis can be realized in such structures. Axiomatically, they are defined by excellent tameness and finiteness properties, which can be applied to problems from analysis. The axiomatic formulation takes place in the language of mathematical logic. O-minimal structures are very important in mathematical fundamental research to understand the connections between geometry, logic and analysis.In the present project, o-minimal structures shall be applied to the following areas from analysis:a) dynamical systems: questions around Hilbert's 16th problem, part 2,b) complex analysis: Riemann mapping theorem,c) potential theory: Dirichlet problem.Interesting relations between these research areas arise thereby.