Modul:   MAT760  Ergodic Theory and Dynamical Systems Seminar

Exact dimension of Oseledets measures

Vortrag von Prof. Dr. François Ledrappier

Sprecher eingeladen von: Prof. Dr. Alexander Gorodnik

Datum: 21.11.22  Zeit: 13.30 - 14.30  Raum: Y27H28

This talk will report on an ongoing joint work with Pablo Lessa (Montevideo). We consider a random walk on a group of matrices. Under suitable assumptions, Oseledets Theorem yields numbers (the Lyapunov exponents) and a random splitting into so-called Oseledets subspaces. This splitting defines a (random) point in a product of Grassmannians. Our Main result is that the distribution of this point is an exact-dimensional measure. The dimension has a geometric interpretation in terms of the exponents and some partial entropies. The talk will present the statement and the main partial results. As an example, we also discuss the case when the random walk is supported by an Anosov 3-dimensional representation of a surface group.