Quantitative recurrence for T, T-1 transformations

• 成果类型: Article
• 署名作者: Pene, Francoise; Saussol, Benoit
• 署名单位: Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01287-z
• 发表日期: 2025
• 页码: 1245-1282
• 关键词: random-walks; limit-theorem; Rare events; times

摘要

We are interested in the study of the asymptotic behaviour of return times in small balls for the T, T-1-transformation. We exhibit different asymptotic behaviour (different scaling, different limit point process) depending on the respective dimensions of the measures of the two underlying dynamical systems. It behaves either as for the direct product of the underlying systems, or as for the Z-extension of the driving system (also studied in this article), or as a more sophisticated process.