Monday 11 Feb 2019: Dynamics Seminar: Computing dynamical invariants and an application to finite continued fractions.
Mark Pollicott - Warwick
For even relatively simple dynamical systems it can be very difficult to get accurate estimates on very basic dynamical quantities (such as Lyapunov exponents, entropy, dimension, variance, etc.). We will describe an efficient method which works for some uniformly hyperbolic systems and allows rigorous estimates on the approximation error. As an illustration, we will consider an application to the density one Zaremba conjecture on finite continued fractions, after Bourgain-Kontorovich and Huang.