论文标题
$ \ mathrm {gl} _n（\ mathbb {r}）$的随机和含义lyapunov指数
Random and mean Lyapunov exponents for $\mathrm{GL}_n(\mathbb{R})$
论文作者
论文摘要
我们考虑在$ \ mathrm {gl} _n（\ Mathbb {r}）$上进行正交的概率度量，并比较矩阵的特征值模量的均值与lyapunov指数的lyapunov指数与随机矩阵产品的lyapunov指数相对于度量的独立绘制。我们就后者提供了一个下限。结果是由dedieu-shub \ cite {ds}激励的。我们治疗的一个新特征是在我们的主要结果证明中使用球形多项式理论。
We consider orthogonally invariant probability measures on $\mathrm{GL}_n(\mathbb{R})$ and compare the mean of the logs of the moduli of eigenvalues of the matrices to the Lyapunov exponents of random matrix products independently drawn with respect to the measure. We give a lower bound for the former in terms of the latter. The results are motivated by Dedieu-Shub\cite{DS}. A novel feature of our treatment is the use of the theory of spherical polynomials in the proof of our main result.
