论文标题
在中间$β$转换的有限类型和匹配的匹配
Subshifts of finite type and matching for intermediate $β$-transformations
论文作者
论文摘要
我们专注于中间$β$转换$ t_ {β，α}（x）=βx+α$（$ \ bmod $ 1）的有限$β$转换之间的匹配和子班次之间的关系，其中$ x \ in [0,1] $ and $（β，α）\ inΔ：=：= \ cy = \ cy = \ c。 \ Mathbb {r}^{2}：β\ in（1，2）\; \ rm {and} \; 0 <α<2-β\} $。我们证明，如果揉捏空间$ω__{β，α} $是有限类型的子迁移，则$ t_ {β，α} $具有匹配。此外，每个$（β，α）\inδ$带有$ t_ {β，α} $具有匹配对应于匹配间隔，并且在光纤上最多有不同的匹配间隔。使用组合方法，我们构建了一对可线化的周期性揉捏不变式，并表明，对于任何$ε> 0 $> 0 $和$（β，α）\inδ$，带有$ t_ {β{β，α} $具有匹配性，存在$（β，α^{\ prime}）$ a $ y-agy的$ | | | | | | | | | | | $ω__{β，α^{\ prime}} $是有限类型的子缩影。结果，$ω_{β，α} $的$（β，α）$是纤维上有限类型的一个子缩影，并且仅当$（β，α）$的集合$ t_ {β，β，α} $的集合在光纤上具有匹配性在光纤上。
We focus on the relationships between matching and subshift of finite type for intermediate $β$-transformations $T_{β,α}(x)=βx+α$ ($\bmod$ 1), where $x\in[0,1]$ and $(β,α) \in Δ:= \{ (β, α) \in \mathbb{R}^{2}:β\in (1, 2) \; \rm{and} \; 0 < α<2 - β\}$. We prove that if the kneading space $Ω_{β,α}$ is a subshift of finite type, then $T_{β,α}$ has matching. Moreover, each $(β,α)\inΔ$ with $T_{β,α}$ has matching corresponds to a matching interval, and there are at most countable different matching intervals on the fiber. Using combinatorial approach, we construct a pair of linearizable periodic kneading invariants and show that, for any $ε>0$ and $(β,α)\inΔ$ with $T_{β,α}$ has matching, there exists $(β,α^{\prime})$ on the fiber with $|α-α^{\prime}|<ε$, such that $Ω_{β,α^{\prime}}$ is a subshift of finite type. As a result, the set of $(β,α)$ for which $Ω_{β,α}$ is a subshift of finite type is dense on the fiber if and only if the set of $(β,α)$ for which $T_{β,α}$ has matching is dense on the fiber.
