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Explore advanced mathematical concepts in this 44-minute lecture from the Simons Semester on Dynamics, delivered by Mark Pollicott from the University of Warwick. Delve into the estimation of dimensions and Lyapunov exponents, beginning with an examination of limit sets for conformal iterated function schemes that satisfy the open set condition. Learn various methodologies for calculating Hausdorff and Box counting dimensions for these sets. Discover practical applications in number theory, specifically focusing on Lagrange spectra through the lens of Matheus and Moreira's work. Investigate the properties of Lyapunov exponents in the context of random matrix products, and conclude with an analysis of their applications to barycentric divisions of triangles.
