Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors
Intrinsic ergodicity beyond specification: β-shifts, S-gap shifts, and their factors
复制标题
超出规范的内在遍历性：β 位移、S 间隙位移及其因子
DOI：
10.1007/s11856-012-0052-x
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发表时间：
2010
影响因子：
1
通讯作者：
D. Thompson
中科院分区：
文献类型：
--
作者：
V. Climenhaga;D. Thompson
我们给出了移位空间（Σ，σ）本质遍历的充分条件，以及Σ的每个子移位因子沿着本质遍历的充分条件。作为一个应用，我们证明了β-移位的每个子移位因子本质上是遍历的，这回答了Mike波义耳的文章“符号动力学中的开放问题”中的一个开放问题.我们得到相同的结果为S-间隙移位，并描述了我们的条件更一般的编码系统的应用。我们的方法的一个新奇是引入了一个新版本的规范属性，很好地适应于研究具有非均匀结构的符号空间。
We give sufficient conditions for a shift space (Σ, σ) to be intrinsically ergodic, along with sufficient conditions for every subshift factor of Σ to be intrinsically ergodic. As an application, we show that every subshift factor of a β-shift is intrinsically ergodic, which answers an open question included in Mike Boyle’s article “Open problems in symbolic dynamics”. We obtain the same result for S-gap shifts, and describe an application of our conditions to more general coded systems. One novelty of our approach is the introduction of a new version of the specification property that is well adapted to the study of symbolic spaces with a non-uniform structure.