时间：2025年3月7日（周五）14:00-15:00
地点：西湖大学云谷校区E4-233
主持人：Lifan Guan, ITS
主讲人：Sanju Velani, University of York
主讲人简介：Professor Sanju Velani graduated in 1991 with a D.Phil. from the University of York. After holding appointments in Göttingen, Imperial College, and Queen Mary Unversity, he has been a professor at the University of York since 2008. Professor Velani's research interests include number theory, dynamical system, and fractral geometry.
讲座主题：Shrinking Targets versus Recurrence
讲座摘要: Let (X,d) be a compact metric space and (X,𝒜,𝜇,T) be a probability measure preserving system. Furthermore, given a real, positive function 𝜓 : ℕ → ℝ≥0 let
R(𝜓) = { x ∈ X : d(Tnx,x) < 𝜓(n) for infinitely many n ∈ ℕ }
denote the associated recurrent set, and given a point x0 ∈ X let
W(𝜓) = { x ∈ X : d(Tnx,x0) < 𝜓(n) for infinitely many n ∈ ℕ }
denote the associated shrinking target set. Under certain mixing properties it known that if the series ∑n ∈ ℕ ψ(n) diverges then both the recurrent and shrinking target sets are of full 𝜇-measure. The purpose of this talk is discuss the potential quantitative strengthening of these full measure statements.
This is joint work with Jason Levesley (York), Bing Li (SCUT) and David Simmons (York), and ongoing work with Junjie Huang (SCUT) and Bing Li (SCUT).
