Branching and self-similarity in group actions

群体行动中的分支和自相似性

• 批准号: DE150100308
• 负责人: Dr Colin Reid
• 金额: $ 19.56万
• 依托单位: The University of Newcastle
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE150100308
• 关键词: Branching; self; similarity; group; actions

This project aims to develop the theory of groups of symmetries that have self-similarity (part of the object has the same structure as the whole) and branching (transformations may be performed on parts of the object independently of one another while preserving the overall structure). The focus will be on a class of topological groups in which these properties frequently occur, building on methods recently developed and their actions on trees and on the Cantor set. The project aims to significantly advance the theory of locally compact groups, as well as giving insights into the phenomena of self-similarity and branching as they occur in group theory and dynamical systems.

该项目旨在发展具有自相似性（对象的一部分具有与整体相同的结构）和分支（在保持整体结构的同时，可以对对象的各部分独立地进行变换）的对称群理论。重点将是一类拓扑群中，这些属性经常发生，建立在最近开发的方法和他们的行动上的树木和康托集。该项目旨在显着推进局部紧群的理论，以及深入了解群论和动力系统中发生的自相似和分支现象。