Applications of a relative variational principle to dimensions of nonconformal expanding maps
Applications of a relative variational principle to dimensions of nonconformal expanding maps
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DOI：
10.1142/s0219493711003486
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发表时间：
2011-11
影响因子：
1.1
通讯作者：
Yuki Yayama
中科院分区：
文献类型：
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作者：
Yuki Yayama
Zhao和Cao（2008）给出了随机动力系统次可加势的相对变分原理。应用他们的结果，我们求出了n（≥3）维广义Sierpinski地毯的Hausdorff维数，它在符号表示中具有不可约sofic移位，并研究了全Hausdorff维数的不变遍历测度.这些结果推广了Kenyon和Peres（1996）关于用全位移表示的n维一般Sierpinski地毯的Hausdorff维数的结果。
Zhao and Cao (2008) showed the relative variational principle for subadditive potentials in random dynamical systems. Applying their result, we find the Hausdorff dimension of an n (≥3)-dimensional general Sierpinski carpet which has an irreducible sofic shift in symbolic representation and study an invariant ergodic measure of full Hausdorff dimension. These generalize the results of Kenyon and Peres (1996) on the Hausdorff dimension of an n-dimensional general Sierpinski carpet represented by a full shift.