Computing leading eigenvalues of the transfer operator

This lecture by the instructor focuses on computing the leading eigenvalue of a transfer operator beyond periodic points. Starting with the linear response theory in physics, the lecture delves into mathematical settings and quantitative problems. It explores the periodic points method for expanding maps, Anosov diffeomorphisms, and the Hausdorff dimension. The transfer operator and spectral radius are discussed, leading to approaches for estimating the spectral radius. The lecture concludes with the Zaremba Conjecture and the dimension of the Cantor set E5. Various steps, including cooking up test functions and verification, are detailed to provide an efficient algorithm for computing the leading eigenvalue.