Integrable system

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In mathematics, integrability is a property of certain dynamical systems, that means very roughly that the solutions of the system are "simple" enough that they can be written down exactly (in principle). More precisely, while there are several distinct formal definitions, an integrable system can be thought of as a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold of much smaller dimensionality than that of its phase space. Integrable systems are in this sense the opposite of chaotic systems, where small changes in initial conditions create wild deviations in the phase space behavior of solutions. Three features are often referred to as characterizing integrable systems: the existence of a maximal set of conserved quantities (the usual defining property of complete integrability) the existence of algebraic invariants, having a basis in algebraic geometry (a property known sometimes as algebraic integrability...

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