Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
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DOI：
10.1007/bf02773211
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发表时间：
2000-12
影响因子：
1
通讯作者：
L. Barreira;J. Schmeling
中科院分区：
文献类型：
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作者：
L. Barreira;J. Schmeling
对于有限型的子移位，共形排斥子，共形马蹄铁，我们证明了点的逐点维数，局部熵，李雅普诺夫指数，和Birkhoff平均值不同时存在的点的集合，进行充分的拓扑熵和充分的Hausdorff维数。这是从一个更强的声明制定了一类符号动力系统，其中包括subshifts规格属性。我们的证明强烈依赖于动力系统的多重分形分析，并构成了这一理论的非平凡的数学应用。
For subshifts of finite type, conformal repellers, and conformal horseshoes, we prove that the set of points where the pointwise dimensions, local entropies, Lyapunov exponents, and Birkhoff averages do not exist simultaneously, carries full topological entropy and full Hausdorff dimension. This follows from a much stronger statement formulated for a class of symbolic dynamical systems which includes subshifts with the specification property. Our proofs strongly rely on the multifractal analysis of dynamical systems and constitute a non-trivial mathematical application of this theory.