These are notes for a series of two talks in the Junior Geometry seminar, Fall 2002, on the proof of Oseledec's multiplicative ergodic theorem as it appeared in a paper of David Ruelle's:

PS, PDF

These are the notes for a single talk to the Working Dynamical Systems Seminar, Spring 2003. This talk contains a better description, I feel, of the Lyapunov exponents, but only states and gives a few comments on the proof of Oseledec's multiplicative ergodic theorem:

PS, PDF