Arnold's Theorem

Arnold's Theorem, in the realm of mathematics and physics, particularly relates to the behavior of dynamical systems. It states that under certain conditions, the motion of objects can be predictable and organized rather than chaotic. Essentially, when a system has enough structure, like certain types of orbits in celestial mechanics, the outcomes can become stable and regular over time. This contrasts with chaotic systems, where small changes can lead to unpredictable results. The theorem emphasizes the balance between randomness and order in complex systems, shedding light on the underlying patterns in seemingly unpredictable behaviors.