### Rigorous techniques for 1D systems (1)

Goldsheid, I *(Queen Mary, London)*

Wednesday 16 July 2008, 14:00-15:30

Seminar Room 1, Newton Institute

#### Abstract

Measure spaces, measure preserving transformations, ergodic transformations, Birkhoff's ergodic theorem, Kingman's sub-additive ergodic theorem. Examples. Products of matrices and Lyapunov exponents: elementary properties. Stationary sequences of random matrices. Products of stationary random matrices: examples. Lyapunov exponents of products of stationary sequences of matrices; the Oseledets's multiplicative ergodic theorem (MOT). The idea of the proof of the MOT; the MOT for products of 2x2 matrices.

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