论文标题
Lyapunov光谱特性和较低关节频谱半径的连续性
Lyapunov spectrum properties and continuity of the lower joint spectral radius
论文作者
论文摘要
我们研究基质共体的lyapunov指数的千古优化和多重分子行为。从某种意义上说，我们在Lyapunov Spectrum的边界上显示了熵光谱的连续性，从某种意义上说，$ h_ {top}（e（α__{t}））\ \ \ \ \ \ rightarrow h_ {top}（e（β（β（\ nabcal {a} a} a}）$用于通用cocycles，$ e（$ e（a） \ lim_ {n \ rightArrow \ infty} \ frac {1} {n} \ log \ | \ | \ Mathcal {a}^{n}（x）\ | =α\ \} $。此外，我们证明了此类共生的差异原理受到限制。 我们证明了在线性共体满足锥体状态的假设下，我们证明了较低的关节光谱半径的连续性。
We study ergodic optimization and multifractal behavior of Lyapunov exponents for matrix cocycles. We show the continuity of the entropy spectrum at the boundary of Lyapunov spectrum in the sense that $h_{top}(E(α_{t}))\ \rightarrow h_{top}(E(β(\mathcal{A}))$ for generic cocycles, where $E(α)=\{x\in X: \lim_{n\rightarrow \infty}\frac{1}{n}\log \|\mathcal{A}^{n}(x)\|=α\}$. We also show that the Lyapunov spectrum is equal to the closure of the set where the entropy spectrum is positive for such cocycles over mixing subshifts of finite type. Moreover, we prove the restricted variational principle for such cocycles. We prove the continuity of the lower joint spectral radius for general cocycles under the assumption that linear cocycles satisfy a cone condition.
