Supercritical holes for the doubling map
نویسنده
چکیده
For a map S : X → X and an open connected set (= a hole) H ⊂ X we define JH(S) to be the set of points in X whose S-orbit avoids H. We say that a hole H0 is supercritical if (i) for any hole H such that H0 ⊂ H the set JH(S) is either empty or contains only fixed points of S; (ii) for any hole H such that H ⊂ H0 the Hausdorff dimension of JH(S) is positive. The purpose of this note is to completely characterize all supercritical holes for the doubling map Tx = 2x mod 1.
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تاریخ انتشار 2012