【摘 要】
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The well-known Dirichlet Theorem in Diophantine approximation states that for any real number x,uniformly for all real numbers Q large than 1,there existsan int
【出 处】
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The 20th International Conference on Difference Equations an
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The well-known Dirichlet Theorem in Diophantine approximation states that for any real number x,uniformly for all real numbers Q large than 1,there existsan integer n between 1 and Q,such that the distance of nx to the nearest integer is less than 1/Q.Consirdered in the unit circle space,the number 0 issaid to be uniformly approximated by the orbit nx of the irrational rotation with the speed 1/Q.In this talk,we will study the numbers uniformly approximatedby orbits of irrational rotations,b-adic and beta-transformations with given polynomial or exponential speed.The Hausdorff dimensions of sets of these uniformly approximated numbers are determined.The talk is based on some joint works with Dong Han KIM and Yann Bugeaud.
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