On badly approximable numbers (Nikolai Moshchevitin, Moscow State University)

It is well known that a real number is badly approximable if and only if the partial quotients in its continued fraction expansion are bounded. Motivated by a recent wonderful paper by Ngoc Ai Van Nguyen, Anthony Poels and Damien Roy (where the authors give a simple alternative solution of Schmidt-Summerer’s problem) we found an unusual generalization of this criterion for badly approximable d-dimensional vectors.