A NOTE ON INHOMOGENEOUS DIOPHANTINE APPROXIMATION

By Yann Bugeaud. Glasgow Mathematical Journal, 2003

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On Exponents of Homogeneous and Inhomogeneous Diophantine Approximation (2005, background): “In higher dimensions, Bugeaud & Chevallier [7] have proved that, for almost all matrices A in M n,m (R) and for any real number w ≥ m/n, we have dim U w (A) = dim{θ ∈ R n : w(A, θ) ≥ w} = m w .”
On shrinking targets for Z^m actions on tori (2008, background): “[4℄ Y. Bugeaud and N. Chevallier, On simultaneous inhomogeneous Diophantine approximation, A taArith.”
The shrinking target problem in the dynamical system of continued fractions (2014, background): “For the irrational rotations on torus, see the work of Bugeaud [4], Troubetzkoy and Schmeling [32], Fan and Wu [9], Bugeaud, Harrap, Kristensen and Velani [5].”