Modified Shrinking Target Problem for Matrix Transformations of Tori
NA YUAN,
SHUAILING WANG
Abstract:In this paper, we calculate the Hausdorff dimension of the fractal set [Formula: see text] where [Formula: see text] is the standard [Formula: see text]-transformation with [Formula: see text], [Formula: see text] is a positive function on [Formula: see text] and [Formula: see text] is the usual metric on the torus [Formula: see text]. Moreover, we investigate a modified version of the shrinking target problem, which unifies the shrinking target problems and quantitative recurrence properties for matrix transf… Show more
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