Shrinking targets versus recurrence: The quantitative theory
Abstract Let , and let be an expanding piecewise linear map sending each interval of linearity to [0,1]. For , , and , we consider the recurrence counting function We show that for any we have for ‐almost all and for all , where . We also prove a generalization of this result to higher dimensions.
Authors
- BING LI (ORCID: https://orcid.org/0000-0003-2976-5616)
- Sanju Velani (ORCID: https://orcid.org/0000-0002-4442-6316)
- David Simmons (ORCID: https://orcid.org/0000-0002-1436-9269)
- Jason Levesley
Institutions
- Science City York (United Kingdom) (GB)
- University of York (GB)
- South China University of Technology (CN)
Publication Details
- Journal
- Mathematika
- Published
- 2025-08-18
- DOI
- https://doi.org/10.1112/mtk.70039
- Citations
- 2
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 7.38
Funders
- National Natural Science Foundation of China
- Natural Science Foundation of Guangdong Province
- National Key Research and Development Program of China