论文标题
动态定义的基质值雅各比操作员的指数二分法
Exponential dichotomy for dynamically defined matrix-valued Jacobi operators
论文作者
论文摘要
我们在这项工作中介绍了在$（\ Mathbb {c}^{l} {l}）中动态定义的矩阵jacobi运算符的指数二分法证明，该二分法给了$ [h_mathbb {c}^{l}）^{\ Mathbb {z}} $，每个$ω\ inω$ in ch $ [h__p textbfffff textbfffff textbffffffextbfffext -1}ω）\ textbf {u} _ {n -1} + d（t^{n}ω）\ textbf {u} _ {n + 1} + v（t^{n}ω）最小同构和$ d，v：ω\ rightarrow m（l，\ mathbb {r}）$是连续的地图，每种$ω\inΩ$都可以使用$ d（ω）$可逆。也就是说，我们表明，对于每个$ω\inΩ$， \ [ρ（h_Ω）= \ {z \ in \ mathbb {c} \ mid（t，a_z）\; \ mathrm {is \;均匀\; $ρ（h_Ω）$是$h_Ω$和$（t，a_z）$的分解集是$ sl（2l，\ mathbb {c}）$ - 由eigenvalue方程$ [h_ _ _ _ n = zu_n $ at $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ at $
We present in this work a proof of the exponential dichotomy for dynamically defined matrix-valued Jacobi operators in $(\mathbb{C}^{l})^{\mathbb{Z}}$, given for each $ω\in Ω$ by the law $[H_ω \textbf{u}]_{n} := D(T^{n - 1}ω) \textbf{u}_{n - 1} + D(T^{n}ω) \textbf{u}_{n + 1} + V(T^{n}ω) \textbf{u}_{n}$, where $Ω$ is a compact metric space, $T: Ω\rightarrow Ω$ is a minimal homeomorphism and $D, V: Ω\rightarrow M(l, \mathbb{R})$ are continuous maps with $D(ω)$ invertible for each $ω\inΩ$. Namely, we show that for each $ω\inΩ$, \[ρ(H_ω)=\{z \in \mathbb{C}\mid (T, A_z)\;\mathrm{is\; uniformly\; hyperbolic}\}, \] where $ρ(H_ω)$ is the resolvent set of $H_ω$ and $(T, A_z)$ is the $SL(2l,\mathbb{C})$-cocycle induced by the eigenvalue equation $[H_ωu]_n=zu_n$ at $z\in\mathbb{C}$.
