Ergodic reduction of random products of two-by-two matrices
Ergodic reduction of random products of two-by-two matrices
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二乘二矩阵的随机乘积的遍历约简
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发表时间：
1997
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通讯作者：
P. Thieullen
中科院分区：
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作者：
P. Thieullen
我们考虑一个抽象动力系统上行列式为1的二乘二矩阵的随机乘积。当两个李雅普诺夫指数不同时，Oseledets定理断言矩阵上循环与对角矩阵上循环是上同调的。当它们相等时，我们证明了上循环共轭于以下三种情况之一：旋转矩阵上循环，上三角矩阵上循环，或对角矩阵上循环模旋转π/2。
We consider a random product of two-by-two matrices of determinant one over an abstract dynamical system. When the two Lyapunov exponents are distinct, Oseledets’ theorem asserts that the matrix cocycle is cohomologous to a diagonal matrix cocycle. When they are equal, we show that the cocycle is conjugate to one of three cases: a rotation matrix cocycle, an upper triangular matrix cocycle, or a diagonal matrix cocycle modulo a rotation by π/2.