Renewal theory and statistics of rare events in infinite ergodic theory

无限遍历理论中稀有事件的更新理论和统计

• 批准号: 229774914
• 负责人: Professor Dr. Marc Keßeböhmer
• 金额: --
• 依托单位: Fachbereich 03: Mathematik und Informatik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/229774914?language=en
• 关键词: Renewal; theory; statistics; rare; events

This research project is dedicated to the investigation of dynamical systems, in particular to the study of infinite ergodic theory. These systems can be characterized as being chaotic (e.g. the dynamic returns typically infinitely often to small sets), but the return time to a given set might be extremely large. It is intended to develop qualitative and quantitative statistical description of the dynamics with the help of functional analytic renewal methods applied to the so-called transfer operator. In particular we are interested to develop extreme value statistics for return times.

本研究项目致力于对动力系统的研究，特别是对无限遍历理论的研究。这些系统可以被描述为混沌的（例如，动态返回通常无限频繁地返回到小集合），但是返回到给定集合的时间可能非常大。它的目的是发展定性和定量的统计描述，帮助泛函分析更新方法应用于所谓的转移算子。我们特别感兴趣的是开发返回时间的极值统计。

项目成果

On the Convergence to Equilibrium of Unbounded Observables Under a Family of Intermittent Interval Maps

断续区间映射族下无界可观测量收敛到平衡

• DOI: 10.1007/s00023-015-0451-8
• 发表时间: 2016
• 期刊: Annales Henri Poincaré
• 作者: J. Kautzsch;M. Kesseböhmer;T. Samuel
• 通讯作者: T. Samuel

On the asymptotics of the α-Farey transfer operator

关于 α-Farey 转移算子的渐近性

• DOI: 10.1088/0951-7715/28/1/143
• 发表时间: 2015
• 期刊: Nonlinearity
• 影响因子: 1.7
• 作者: J. Kautzsch;M. Kesseböhmer;T. Samuel;B. O. Stratmann
• 通讯作者: B. O. Stratmann