Estimates on Hausdorff dimension and Lyapunov exponents and their applications.

Speaker. Mark Pollicott
Date. 25.10.22 at 3:30 pm

Abstract. We will consider 2 classical questions:
(a) Given an iterated function scheme of contractions (on the unit interval), what is the Hausdorff dimension of the limit set?
(b) Given a random product of finitely many matrices, what is the (largest) Lyapunov exponent?
We will motivate this by simple applications to (a) Number Theory; and (b) Euclidean and Hyperbolic Geometry.