On the Veronese curve in R^3, the set of simultaneously lambda-well approximable points has Hausdorff dimension (2-2lambda)/(1+lambda) for all 1/3 <= lambda <= 3/5.
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Simultaneous Diophantine approximation on the three dimensional Veronese curve
On the Veronese curve in R^3, the set of simultaneously lambda-well approximable points has Hausdorff dimension (2-2lambda)/(1+lambda) for all 1/3 <= lambda <= 3/5.