Grassmannian上的部分双曲型随机动力学
Partially hyperbolic random dynamics on Grassmannians
摘要：
由固定对角部分双曲矩阵周围的小随机扰动给出的可逆矩阵序列在格拉斯曼流形上诱导随机动力学。在适当的弱条件下，已知它有唯一的不变（Furstenberg）测度。主要结果给出了浓度界限上的这一措施表明，以高概率的随机动态停留在附近的稳定不动点的未扰动矩阵，在政权的随机扰动的强度占主导地位的对角矩阵的局部双曲性。作为应用，得到了李雅普诺夫指数和的界.
英文摘要：
A sequence of invertible matrices given by a small random perturbation around a fixed diagonal partially hyperbolic matrix induces a random dynamics on the Grassmann manifolds. Under suitable weak conditions it is known to have a unique invariant (Furstenberg) measure. The main result gives concentration bounds on this measure showing that with high probability the random dynamics stays in the vicinity of stable fixed points of the unperturbed matrix, in a regime where the strength of the random perturbation dominates the local hyperbolicity of the diagonal matrix. As an application, bounds on sums of Lyapunov exponents are obtained.
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