# Mathematics Colloquia and Seminars

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### Towards a constructive approach to Lyapunov exponents.

**Mathematical Physics & Probability**

Speaker: | Ilya Goldsheid, UC Davis |

Location: | 693 Kerr |

Start time: | Tue, Apr 20 2004, 3:10PM |

Abstract. The classical result by Furstenberg (1963) states that if certain mild conditions are satisfied then products of i.i.d. random matrices from SL(m,R) grow exponentially fast. The classical result by Furstenberg (1963) states that if certain mild conditions are satisfied then products of i.i.d. random matrices from SL(m,R) grow exponentially fast. This fact plays a crucial role in many applications of the theory of products of random matrices. However there are many problems (in particular in mathematical physics) for which one needs constructive estimates for Lyapunov exponents. I shall discuss several problems of this sort and explain an approach leading to their solution.