Ergodic reduction of random products of two-by-two matrices
- Cite this article as:
- Thieullen, P. J. Anal. Math. (1997) 73: 19. doi:10.1007/BF02788137
- 125 Downloads
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.