All Outputs (2)

Thue-Morse constant is not badly approximable (2014)
Journal Article
Badziahin, D., & Zorin, E. (2015). Thue-Morse constant is not badly approximable. International Mathematics Research Notices, 2015(19), 9618-9637. https://doi.org/10.1093/imrn/rnu238

We prove that Thue–Morse constant τTM=0.01101001…2 is not a badly approximable number. Moreover, we prove that τTM(a)=0.01101001…a is not badly approximable for every integer base a≥2 such that a is not divisible by 15. At the same time, we provide a... Read More about Thue-Morse constant is not badly approximable.

Badly approximable points on planar curves and a problem of Davenport (2014)
Journal Article
Badziahin, D., & Velani, S. (2014). Badly approximable points on planar curves and a problem of Davenport. Mathematische Annalen, 359(3-4), 969-1023. https://doi.org/10.1007/s00208-014-1020-z

Let C be two times continuously differentiable curve in R2 with at least one point at which the curvature is non-zero. For any i,j⩾0 with i+j=1, let Bad(i,j) denote the set of points (x,y)∈R2 for which max{∥qx∥1/i,∥qy∥1/j}>c/q for all q∈N. Here c=c(x... Read More about Badly approximable points on planar curves and a problem of Davenport.