Integrability

Integrability refers to the property of a system, often mathematical or physical, that allows it to be exactly solved or understood through precise methods. In such systems, you can find complete solutions that describe their behavior over time using a set of well-defined equations. This typically involves first identifying quantities called integrals of motion—constants that stay unchanged—which simplifies the analysis. Integrable systems are predictable and orderly, unlike chaotic systems. Overall, integrability means we can fully determine how a system evolves based on fundamental principles, enabling deep insights into its dynamics.