Supercritical Holes for the Doubling Map

作者：Sidorov N^*

来源：Acta Mathematica Hungarica, 2014, 143(2): 298-312.

DOI：10.1007/s10474-014-0403-7

• open dynamical system
• doubling map
• Sturmian system
• characteristic word
• supercritical hole

For a map S : X -> X and an open connected set (= a hole) H subset of X we define J(H)(S) to be the set of points in X whose S-orbit avoids H. We say that a hole H-0 is supercritical if (i) for any hole H such that (H) over bar (0) subset of H the set J(H)(S) is either empty or contains only fixed points of S; (ii) for any hole H such that (H) over bar subset of H-0 the Hausdorff dimension of J(H)(S) is positive. The purpose of this note is to completely characterize all supercritical holes for the doubling map Tx = 2x mod 1.

• 出版日期2014-8