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-极小结构及其在动力系统、复分析和位势理论中的应用。O-极小结构推广了代数型几何。来自分析的重要概念和功能可以在这样的结构中实现。从公理上讲，它们是由优秀的驯服和有限性质定义的，这些性质可以应用于分析问题。公理的表述是在数理逻辑的语言中进行的。O-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是非常重要的。在本项目中，O-极小结构将从分析应用到下列领域：a)动力系统：围绕Hilbert第16问题的问题，第二部分，b)复分析：Riemann映射定理，c)位势理论：Dirichlet问题。由此产生了这些研究领域之间的有趣关系。

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.