For a two-dimensional shrinking target set in a beta-dynamical system, the Hausdorff dimension equals min{s1,s2}, where s1 and s2 are the first roots of two pressure-function inequalities.
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Higher dimensional shrinking target problem in beta dynamical systems
For a two-dimensional shrinking target set in a beta-dynamical system, the Hausdorff dimension equals min{s1,s2}, where s1 and s2 are the first roots of two pressure-function inequalities.