Uniform Diophantine approximation in continued fractions
Date:
Wednesday, 7 August, 2024 - 16:30 - 17:30
Venue:
LSB 219
Seminar Type:
Analysis Seminar Talks-Mini workshop on Fractals and Related Topics
Speaker Name:
Prof. Qinglong Zhou
Affiliation:
Wuhan University of Technology
Abstract:
We consider the multifractal properties of the asymptotic and uniform approximation exponent in continued fractions. As a corollary, we determine the Hausdorff dimension of uniform Diophantine set
{x ∈ [0, 1) : ∀N≥ 1, ∃n ∈ [1, N ], s.t |T n(x) − y| < |IN (y)|vˆ}
for a class of quadratic irrational numbers y.
Poster:
