科研之友
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摘要
We consider the asymptotic behaviors of the orbits of an expanding Markov system ([0, 1],f), and prove that the badly approximable set @@@ {x is an element of [0, 1) :lim inf(n ->infinity) vertical bar f(n)(x) - y(n)vertical bar > 0}, @@@ is of full Hausdorff dimension for any given sequence {y(n)}(n >= 0) subset of [0, 1]. Consequently, the Hansdorff dimension of the set of nonrecurrent points in the sense that {x is an element of [0, 1] :liminf(n ->infinity)vertical bar f(n)(x) - x vertical bar > 0} is also full. The results can be applied to beta-transformations, Gauss maps and Luroth maps, etc.
