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Exact Approximation Order and Well-distributed Sets by Bandi, Prasuna; Ghosh, Anish; Nandi, Debanjan is a scholarly article available to read on EtoBox.

What is Exact Approximation Order and Well-distributed Sets about?

We prove that for any proper metric space $X$ and a function $\psi:(0,\infty)\to(0,\infty)$ from a suitable class of approximation functions, the Hausdorff dimensions of the set $W_\psi(Q)$ of all points $\psi$-well-approximable by a well-distributed subset $Q\subset X$, and the set $E_\psi(Q)$ of points that are exactly $\psi$-approximable by $Q$, coincide. This answers in a general setting, a question of Beresnevich-Dickinson-Velani in the case of approximation of reals by rationals, and answered by Bugeaud in that case using the continued-fraction expansion of reals. Our main result applies in particular to approximation by orbits of fixed points of a wide class of discrete groups of isometries acting on the boundary of hyperbolic metric spaces.

Author

Bandi, Prasuna; Ghosh, Anish; Nandi, Debanjan

Published

2022

Language

EN