Introduction to KAM Theory - Lecture 2

Explore a comprehensive lecture on Kolmogorov-Arnold-Moser (KAM) theory and its application to the persistence of quasi-periodic motions in dynamical systems. Delve into the fundamental stability questions in celestial mechanics that have captivated astronomers, physicists, and mathematicians for centuries. Learn how to approach these problems through perturbative methods and understand the challenges in establishing convergence of formal series expansions due to small divisors. Master the essential techniques of KAM theory that provide solutions to these complex mathematical challenges. Begin with a detailed examination of analytic circle diffeomorphisms near circle rotations as a foundational example, before advancing to explore the theory's classical applications in Hamiltonian dynamical systems. Part of the Simons Semester on Dynamics series, this hour-long lecture provides a rigorous mathematical framework for understanding the persistence of quasi-periodic motions in dynamical systems.