KAM Theory

Kolmogorov-Arnold-Moser (KAM) Theory studies how systems with many small, interacting parts — like celestial bodies or complex mechanical systems — behave over time. It shows that if the system's parameters are only slightly changed, many of its regular, predictable orbits or motions remain stable, forming KAM tori (invariant surfaces). These stable structures help explain why some orbits stay consistent despite small disturbances, while others may become chaotic. Overall, KAM Theory provides a mathematical foundation for understanding the persistence of order within complex, near-integrable systems.