Journal d’Analyse Mathématique

, Volume 73, Issue 1, pp 19–64

Ergodic reduction of random products of two-by-two matrices

  • Ph. Thieullen

DOI: 10.1007/BF02788137

Cite this article as:
Thieullen, P. J. Anal. Math. (1997) 73: 19. doi:10.1007/BF02788137


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.

Copyright information

© Hebrew University of Jerusalem 1997

Authors and Affiliations

  • Ph. Thieullen
    • 1
  1. 1.Département de MathématiquesUniversité Paris-SudOrsay CedexFrance