"Measure-theoretic dimension groups, classification of ergodic transformation, and topics in positivity"

“测度论维度组、遍历变换的分类以及积极性主题”

• 批准号: 3130-2012
• 负责人: Handelman, David
• 金额: $ 0.87万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=544082
• 关键词: Measure; theoretic; dimension; groups; classification

A new invariant, a "dimension space", developed (2009) by Giordano and me for classifying (measure-theoretically) dynamical systems leads to new results, questions, novel directions of research, and to other areas of mathematics. The project is mostly concerned with developing a lexicon between properties of ergodic transformations and (more algebraic/functional analytic) properties of dimension spaces, so that properties that are more easily seen in one context can be be translated to the other.

2009年，佐丹奴和我开发了一种新的不变量，即“维度空间”，用于对（理论上的）动力系统进行分类，从而产生了新的结果、问题、新的研究方向以及数学的其他领域。该项目主要关注开发遍历变换属性和维度空间（更多的代数/泛函分析）属性之间的词典，以便在一种上下文中更容易看到的属性可以转换到另一种上下文中。