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For any j_1,...,j_n>0 with j_1+...+j_n=1 and any x \in R^n, we consider theset of points y \in R^n for which max_{1\leq i\leq n}(||qx_i-y_i||^{1/j_i})>c/qfor some positive constant c=c(y) and all q\in N. These sets are the `twisted'inhomogeneous analogue of Bad(j_1,...,j_n) in the theory of simultaneousDiophantine approximation. It has been shown that they have full Hausdorffdimension in the non-weighted setting, i.e provided that j_i=1/n, and in theweighted setting when x is chosen from Bad(j_1,...,j_n). We generalise theseresults proving the full Hausdorff dimension in the weighted setting withoutany condition on x.

Badly approximable points in twisted Diophantine approximation and Hausdorff dimension