论文标题
Univoque序列频率集的Hausdorff尺寸
Hausdorff dimension of frequency sets of univoque sequences
论文作者
论文摘要
对于Integer $ M \ GE3 $，我们研究动力系统$（λ_m，σ_m）$其中$λ_m$是set $ \ {w \ in \ {0,1 \}^\ mathbb {n}： $ \ {0,1 \}^\ mathbb {n} $仅限于$λ_m$，在$λ_M$上研究Bernoulli-Type测量，并找出唯一的等价$σ_M$ $σ_M$ -INVARIANT ERGODIC概率指标。作为应用程序，我们获得了Univoque序列集的Hausdorff尺寸，即连续$ 0 $ 0 $'的长度和连续$ 1 $的序列的Hausdorff维度，其频率subset的频率尺寸。
For integer $m\ge3$, we study the dynamical system $(Λ_m,σ_m)$ where $Λ_m$ is the set $\{w\in\{0,1\}^\mathbb{N}: w$ does not contain $0^m$ or $1^m\}$ and $σ_m$ is the shift map on $\{0,1\}^\mathbb{N}$ restricted to $Λ_m$, study the Bernoulli-type measures on $Λ_m$ and find out the unique equivalent $σ_m$-invariant ergodic probability measure. As an application, we obtain the Hausdorff dimension of the set of univoque sequences, the Hausdorff dimension of the set of sequences in which the lengths of consecutive $0$'s and consecutive $1$'s are bounded, and the Hausdorff dimension of their frequency subsets.
