Absolutely Continuous Invariant Measures for Selectors of Multivalued Maps and Their Applications

多值映射选择器的绝对连续不变测度及其应用

• 批准号: RGPIN-2015-03708
• 负责人: Gora, Pawel
• 金额: $ 1.02万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635328
• 关键词: Absolutely; Continuous; Invariant; Measures; Selectors

A Multi-Valued Map (MVM) is a function whose values are subsets of a space rather than individual elements of the space. The main objective of my research is to study the long term statistical behaviour of dynamical systems defined by a MVM. This approach is the basic method of Ergodic Theory in which I specialize. Ergodic Theory is now an established and active research area (four of fourteen Fields medalists in this century were recognized for their contributions to Ergodic Theory).

多值映射(MVM)是指其值是空间的子集而不是空间的单个元素的函数。我研究的主要目的是研究由MVM定义的动力系统的长期统计行为。这种方法是我专门研究的遍历理论的基本方法。遍历理论现在是一个成熟而活跃的研究领域(本世纪14位菲尔兹奖牌获得者中有4位因其对遍历理论的贡献而受到认可)。