摘要
Let T:T^(d)→T^(d),defined by Tx=AX(mod 1),where A is a d×d integer matrix with eigenvalues 1<|λ_(1)|≤|λ_(2)|≤…≤|λ_(d)|,We investigate the Hausdorff dimension of the recurrence set R(ψ)={x∈T^(d):T^(n)x∈B(x,ψ(n))for infinitely many n}forα≥log|λ_(d)/λ_(1)|,whereψis a positive decreasing function defined onℕand its lower order at infinity isα=lim inf_(n→∞)-logψ(n)/n.In the case that A is diagonalizable overℚwith integral eigenvalues,we obtain the dimension formula.
基金
supported by the Science Foundation of China University of Petroleum,Beijing(2462023SZBH013)
the China Postdoctoral Science Foundation(2023M743878)
the Postdoctoral Fellowship Program of CPSF(GZB20240848)
supported partially by the NSFC(12271176)
the Guangdong Natural Science Foundation(2024A1515010946).
