论文标题
自由单粒形态引起的亚缩的测量转移
The measure transfer for subshifts induced by a morphism of free monoids
论文作者
论文摘要
每个非序列的单体形态$σ：\ Mathcal {a}^* \ to \ nathcal {b}^* $诱导A {\ em量度传输映射} $σ_x^{\ MATHCAL {M MATHCAL {M MATHCAL {M MATHCAL {M MATHCAL {m} $ \ MATHCAL {M}（X）$和$ \ MATHCAL {M}（σ（x））$，与任何子缩影$ x \ subset \ subset \ mathcal {a}^{\ mathbb {z}} $及其image subshift $ subshift $ x（x）\ subset \ subset \ mathcal} 分别。我们详细定义并研究了这张地图，并表明它是连续的，线性和功能的。事实证明，它也是过渡性\ cite {bhl2.8-ii}。此外，提出了一种有效的技术，用于计算任何圆柱体$ [w] $上转移的度量$σ_x^{\ Mathcal {m}（m）} $（用于$ w \ in \ Mathcal {B}^*$）。 \ smallskip \ noindent {\ bf theorem：}如果非射击态度$σ：\ Mathcal {a}^* \ to \ natercal {b}^* $是在某个子shift $ x \ subset \ subset \ subset \ subset \ subset \ subset \ subset \ nath $ nath的移位上的imptive $σ^{\ Mathcal {m} _x} $是iNjective。 \ smallskip $σ$的假设是``在$ x $''的移位范围内的注入''严格弱于``$ x $''的``可识别''，并且严格比````''''''''''。最后一个假设通常不足以获得测量传输映射的注入性$σ_x^{\ Mathcal {m}} $。
Every non-erasing monoid morphism $σ: \mathcal{A}^* \to \mathcal{B}^*$ induces a {\em measure transfer map} $σ_X^{\mathcal{M}}: \mathcal{M}(X) \to \mathcal{M}(σ(X))$ between the measure cones $\mathcal{M}(X)$ and $\mathcal{M}(σ(X))$, associated to any subshift $X \subset \mathcal{A}^{\mathbb{Z}}$ and its image subshift $σ(X) \subset \mathcal{B}^{\mathbb{Z}}$ respectively. We define and study this map in detail and show that it is continuous, linear and functorial. It also turns out to be surjective \cite{BHL2.8-II}. Furthermore, an efficient technique to compute the value of the transferred measure $σ_X^{\mathcal{M}(μ)}$ on any cylinder $[w]$ (for $w \in \mathcal{B}^*$) is presented. \smallskip \noindent {\bf Theorem:} If a non-erasing morphism $σ: \mathcal{A}^* \to \mathcal{B}^*$ is injective on the shift-orbits of some subshift $X \subset \mathcal{A}^\mathbb{Z}$, then $σ^{\mathcal{M}_X}$ is injective. \smallskip The assumption on $σ$ that it is ``injective on the shift-orbits of $X$'' is strictly weaker than ``recognizable in $X$'', and strictly stronger than ``recognizable for aperiodic points in $X$''. The last assumption does in general not suffice to obtain the injectivity of the measure transfer map $σ_X^{\mathcal{M}}$.
