Watch a 51-minute mathematics lecture exploring advanced concepts in dynamical systems and their applications, delivered by Mark Pollicott from the University of Warwick as part of the Simons Semester on Dynamics. Learn about limit sets for conformal iterated function schemes with open set conditions and discover various methods for calculating Hausdorff and Box counting dimensions. Explore practical applications in number theory through Lagrange spectra analysis, understand Lyapunov exponents in the context of random matrix products, and examine their relevance to barycentric divisions of triangles.