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

O-最小结构及其在动力系统、复杂分析和势理论中的应用

• 批准号: 183020239
• 负责人: Professor Dr. Tobias Kaiser
• 金额: --
• 依托单位: Professur für Reine Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/183020239?language=en
• 关键词: minimal; Structures; their; Applications; Dynamical

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.

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。

项目成果

Global complexification of real analytic globally subanalytic functions

实解析全局子解析函数的全局复杂化

• DOI: 10.1007/s11856-016-1306-9
• 发表时间: 2016
• 期刊: Israel Journal of Mathematics
• 影响因子: 1
• 作者: T. Kaiser

Multivariate Puiseux Rings Induced by a Weierstrass System and Twisted Group Rings

Weierstrass 系统和扭曲群环诱导的多元 Puiseux 环

• DOI: 10.1080/00927872.2013.816314
• 发表时间: 2014
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: T. Kaiser

Integration of semialgebraic functions and integrated Nash functions

半代数函数和积分纳什函数的积分

• DOI: 10.1007/s00209-012-1138-1
• 发表时间: 2013
• 期刊: Mathematische Zeitschrift
• 影响因子: 0.8
• 作者: T. Kaiser