Work

Shrinking targets versus recurrence: The quantitative theory

Year: 2025

Type: article

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.

Source: Mathematika

DOI: 10.1112/mtk.70039

Authors: Jason Levesley, Bing Li, David Simmons, Sanju Velani

Institutions: University of York, South China University of Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Guangdong Province, National Key Research and Development Program of China

Awards: G3209938231, G5711158969, G8927595000