Year: 2025
Type: article
Abstract: Let be an invertible matrix with integer elements. Then determines a self‐map of the ‐dimensional torus . Given a real number , and a sequence of points in , let be the set of points such that for infinitely many . The Hausdorff dimension of has previously been studied by Hill–Velani and Li–Liao–Velani–Zorin. We provide a lower bound on the Hausdorff dimension of for any expanding matrix. For hyperbolic matrices, we compute the dimension of only when is a matrix. We give counterexamples to a natural candidate for a dimension formula for general dimension .
DOI: 10.1112/jlms.70287
Authors: Zhang‐nan Hu, Tomas Persson, Wanlou Wu, Yiwei Zhang
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation, China University of Petroleum, Beijing, Government of Jiangsu Province, Natural Science Foundation of Jiangsu Province, Science Foundation of China University of Petroleum, Beijing, Basic and Applied Basic Research Foundation of Guangdong Province
OpenAlex ID: W4414086276