Introduction to KAM Theory - Lecture 1

Explore the fundamentals of Kolmogorov-Arnold-Moser (KAM) theory in this one-hour lecture focusing on the persistence of quasi-periodic motions. Delve into stability questions in celestial mechanics that have captivated astronomers, physicists, and mathematicians for centuries. Learn how to approach perturbative problems and understand the challenges of formal series expansions due to small divisors. Master the essential techniques of KAM theory through detailed examination of analytic circle diffeomorphism linearization near circle rotation. Conclude with an introduction to KAM theory's applications in Hamiltonian dynamical systems, gaining valuable insights into this powerful mathematical framework for understanding stability in mechanical systems.