KAM Theory (Kolmogorov-Arnold-Moser Theory)

KAM Theory, or Kolmogorov-Arnold-Moser Theory, explains how many complex, nearly regular systems—like planets orbiting a star—remain stable despite small disturbances. It shows that in certain conditions, these systems preserve a structured, predictable pattern called quasi-periodic motion, thanks to special surfaces called invariant tori in their phase space. Essentially, it demonstrates that small changes won't always cause chaos; instead, many parts of the system stay stable, maintaining their overall behavior over time. This theory helps explain why some orbits and dynamical systems remain orderly even amidst minor influences.