Oseledec’s Multiplicative Ergodic Theorem
نویسنده
چکیده
These are notes for a talk in the Junior Geometry seminar at UT Austin on Oseledec’s multiplicative ergodic theorem given in Fall 2002. The purpose of the notes is to insure that I know, or at least am convinced that I think I know, what I am talking about. They contain far more material than the talks themselves, constituting a complete proof of the discrete-time version of the multiplicative ergodic theorem. Perhaps sometime in the future I will work through the argument required to adapt that proof to the continuoustime version of the theorem. To motivate the theorem, I start with a discussion of Lyapunov exponents, whose existence follows from an application of the continuous-time multiplicative ergodic theorem to the differential map on the tangent bundle of a compact Riemannian manifold. Since the intended audience for the talk was geometers, I felt this motivation was needed. I then give a proof of the multiplicative ergodic theorem that closely follows [1], though I have filled in quite a large number of details.
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